Numerical methods of statistics, second edition

Numerical Methods of Statistics, Second Edition

Volumn , Issue , 2011, Pages 1-447

  Monahan, John F ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84924699841     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511977176     Document Type: Book

References (401)

1. Robert Gentleman and Ross Ihaka (2000), “Lexical Scope and Statistical Computing.” Journal of Computational and Graphical Statistics9: 491–508.
2. Donald E. Knuth (1997), The Art of Computer Programming(vol. 1: Fundamental Algorithms), 3rd ed. Reading, MA: Addison-Wesley.
3. Mark Priestly (1997), Practical Object-Oriented Design. London: McGraw-Hill.
4. Gotz Alefeld and Jurgen Herzberger (1983), Introduction to Interval Computations. New York: Academic Press.
5. Peter Alfeld and David J. Eyre (1991), “The Exact Analysis of Sparse Rectangular Systems,” ACM Transactions on Mathematical Software17: 502–18.
6. Anonymous (1956), Number Systems. Poughkeepsie, NY: IBM Corporation.
7. David H. Bailey (1988), “The Computation of π to 29,360,000 Decimal Digits Using Borweins’ Quartically Convergent Algorithm,” Mathematics of Computation50: 283–96.
8. Richard P. Brent (1978), “A Fortran Multiple-Precision Arithmetic Package,” ACM Transactions on Mathematical Software4: 57–70.
9. W. J. Cody (1988), “Algorithm 665, MACHAR: A Subroutine to Dynamically Determine Machine Parameters,” ACM Transactions on Mathematical Software14: 303–11.
10. Germund Dahlquist and Ake Bjorck (1974), Numerical Methods(trans. by N. Anderson). Englewood Cliffs, NJ: Prentice-Hall.
11. T. J. Dekker (1971), “A Floating-Point Technique for Extending theAvailable Precision,” Numerische Mathematik18: 224–42.
12. George E. Forsythe, Michael A. Malcolm, and Cleve B. Moler (1977), Computer Methods for Mathematical Computations. Englewood Cliffs, NJ: Prentice-Hall.
13. David Goldberg (1991), “What Every Computer Scientist Should Know about Floating Point Arithmetic,” ACM Computing Surveys23: 5–48.
14. Institute of Electrical and Electronics Engineers (1985), “IEEE Standard for Binary Floating Point Arithmetic,” Standard 754-1985, IEEE, New York.
15. W. Kahan, J. Palmer, and J. Coonen (1979), “A Proposed IEEE-CS Standard for Binary Floating Point Arithmetic,” Proceedings of the Twelfth Interface Symposium on Computer Science and Statistics, pp. 32–6, University of Waterloo.
16. Sallie Keller-McNulty and William J. Kennedy (1985), “Error-free Computation of a Reflexive Generalized Inverse,” Linear Algebra and Its Applications 67: 157–67.
17. Donald E. Knuth (1997a), The Art of Computer Programming(vol. 1: Fundamental Algorithms), 3rd ed. Reading, MA: Addison-Wesley.
18. Donald E. Knuth (1997b), The Art of Computer Programming(vol. 2: Seminumerical Algorithms), 3rd. ed. Reading, MA: Addison-Wesley.
19. Ulrich W. Kulisch and Willard L. Miranker (1981), Computer Arithmetic in Theory and Practice. New York: Academic Press.
20. R. S. Martin, G. Peters, and J. H. Wilkinson (1965), “Symmetric Decomposition of a Positive Definite Matrix,” Numerische Mathematik7: 363–83.
21. Ramon E. Moore (1979), Methods and Applications of Interval Analysis. Philadelphia: SIAM.
22. Michael L. Overton (2001), Numerical Computing with IEEE Floating Point Arithmetic; Philadelphia: SIAM.
23. Stephen K. Park and Keith W. Miller (1988), “Random Number Generators: Good Ones Are Hard to Find,” Communications of the ACM31: 1192–1201.
24. H. L. Royden (1968), Real Analysis, 2nd ed. New York: Macmillan.
25. Paul A. Samuelson (1968), “How Deviant Can You Be?” Journal of the American Statistical Association63: 1522–5.
26. David M. Smith (1991), “Algorithm 693: A Fortran Package for Floating-Point Multiple-Precision Arithmetic,” ACM Transactions on Mathematical Software17: 273–83.
27. G.W. Stewart (1973), Introduction to Matrix Computations. New York: Academic Press.
28. Nai-kuan Tsao (1974), “On the Distribution of Significant Digits and Roundoff Errors,” Communications of the ACM17: 269–271.
29. Morgan C. Wang and William J. Kennedy (1994), “Self-Validating Computations of Probabilities for Selected Central and Noncentral Univariate Probability Functions,” Journal of the American Statistical Association89: 878–87.
30. J. H. Wilkinson and C. Reinsch (Eds.) (1971), Linear Algebra. New York: Springer-Verlag.
31. E. Anderson, Z. Bai, C. Bishof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorenson (1995), LAPACK Users’ Guide. Philadelphia: SIAM.
32. A. K. Cline, C. B. Moler, G.W. Stewart, and J. H. Wilkinson (1979), “An Estimate for the Condition Number of a Matrix,” SIAM Journal of Numerical Analysis16: 368–75.
33. James W. Demmel (1988), “The Probability That a Numerical Analysis Problem Is Difficult,” Mathematics of Computation50: 449–80.
34. J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart (1979), LINPACK Users’ Guide. Philadelphia: SIAM.
35. Gene H. Golub and Charles van Loan (1996), Matrix Computations, 3rd. ed. Baltimore: Johns Hopkins University Press.
36. Alton S. Householder (1975), The Theory of Matrices in Numerical Analysis. New York: Dover.
37. Ilse C. F. Ipsen (2009), Numerical Matrix Analysis. Philadelphia: SIAM.
38. Alan Jennings (1977), Matrix Computation for Engineers and Scientists. New York: Wiley.
39. Donald E. Knuth (1997), The Art of Computer Programming(vol. 1: Fundamental Algorithms), 3rd ed. Reading, MA: Addison-Wesley.
40. Peter Lancaster and Miron Tismenetsky (1985), The Theory of Matrices, 2nd ed. Orlando, FL: Academic Press.
41. G.W. Stewart (1973), Introduction to Matrix Computations. New York: Academic Press.
42. G.W. Stewart (1980), “The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators,” SIAM Journal of Numerical Analysis17: 403–9.
43. G.W. Stewart and Ji-guang Sun (1990), Matrix Perturbation Theory. Boston: Academic Press.
44. Craig F. Ansley (1979), “An Algorithm for the Exact Likelihood of a Mixed Autoregressive-Moving Average Process,” Biometrika66: 59–65.
45. Richard H. Bartels and Gene H. Golub (1969), “The Simplex Method of Linear Programming Using LU Decomposition,” Communications of the ACM, 12: 266–68.
46. G. E. P. Box and G.M. Jenkins (1972), Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.
47. George Cybenko (1980), “The Numerical Stability of the Levinson–Durbin Algorithm for Toeplitz Systems of Equations,” SIAM Journal of Scientific and Statistical Computing1: 303–19.
48. J. Durbin (1960), “The Fitting of Time Series Models,” Revue Internationale Institut de Statistique28: 233–43.
49. Gene H. Golub and Charles van Loan (1996), Matrix Computations, 3rd ed. Baltimore: Johns Hopkins University Press.
50. W. J. Harrod and R. J. Plemmons (1984), “Comparison of Some Direct Methods for Computing Stationary Distributions of Markov Chains,” SIAM Journal of Scientific and Statistical Computing5: 453–69.
51. John Haslett and Adrian Raftery (1989), “Space-Time Modelling with Long-Memory Dependence: Assessing Ireland’s Wind Power Resource,” Applied Statistics38: 1–50.
52. J. R. M. Hosking (1981), “Fractional Differencing,” Biometrika68: 165–76.
53. Alan Jennings (1977), Matrix Computation for Engineers and Scientists. New York: Wiley.
54. C. T. Kelley (1995), Iterative Methods for Linear and Nonlinear Equations. Philadelphia: SIAM.
55. Norman Levinson (1947), “The Weiner RMS Error Criterion in Filter Design and Prediction,” Journal of Mathematics and Physics26: 261–78.
56. R. S. Martin and J. H. Wilkinson (1965), “Symmetric Decomposition of Positive Definite Band Matrices,” Numerische Mathematik7: 355–61.
57. John F. Monahan (1984), “A Note on Enforcing Stationarity in Autoregressive-Moving Average Models,” Biometrika71: 403–4.
58. Bruce A. Murtagh (1981), Advanced Linear ProgrammingNew York: McGraw-Hill.
59. Marcello Pagano (1973), “When is an Autoregressive Scheme Stationary?” Communications in Statistics1: 533–44.
60. William F. Trench (1964), “An Algorithm for the Inversion of Finite Toeplitz Matrices,” Journal of SIAM12: 515–22.
61. Albert E. Beaton (1977), “Comment on ‘More on Computational Accuracy in Regression’,” Journal of the American Statistical Association72: 600.
62. Albert E. Beaton, Donald B. Rubin, and John L. Barone (1976), “The Acceptability of Regression Solutions: Another Look at Computational Accuracy,” Journal of the American Statistical Association71: 158–68.
63. D. A. Belsley, E. Kuh, and R. E. Welsch (1980), Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: Wiley.
64. Ake Bjorck (1967), “Solving Least Squares Problems by Gram–Schmidt Orthogonalization,” BIT7: 1–21.
65. K. A. Brownlee (1965), Statistical Theory and Methodology in Science and Engineering, 2nd ed. New York: Wiley.
66. Tony F. Chan, Gene H. Golub, and Randall J. LeVeque (1983), “Algorithms for Computing the Sample Variance,” American Statistician37: 242–7.
67. M. R. B. Clarke (1981), “AS 163:AGivens Algorithm for Moving from One Linear Model to Another without Going Back to the Data,” Applied Statistics30: 198–203.
68. R. D. Cook and S. Weisberg (1982), Residuals and Influence in Regression. New York: Chapman & Hall.
69. Germund Dahlquist and Ake Bjorck (1974), Numerical Methods(trans. by N. Anderson). Englewood Cliffs, NJ: Prentice-Hall.
70. M. H. Doolittle (1878), United States Coast Guard and Geodetic Survey Report, vol. 115.
71. Bradley Efron, Trevor Hastie, Iain Johnstone, and Robert Tibshirani (2004), “Least Angle Regression,” Annals of Statistics32: 407–499.
72. R. J. Freund (1979), “Multicollinearity etc., Some ‘New’ Examples,” in Proceedings of the Statistical Computing Section, pp. 111–12. Washington, DC: American Statistical Association.
73. George M. Furnival (1971), “All Possible Regressions with Less Computation,” Technometrics13: 403–8.
74. George M. Furnival and Robert W. Wilson, Jr. (1974), “Regressions by Leaps and Bounds,” Technometrics16: 499–511.
75. W. Morven Gentleman (1973), “Least Squares Computations by Givens Transformations without Square Roots,” Journal of the Institute of Mathematics and Its Applications12: 329–36.
76. Philip E. Gill and Walter Murray (1978), “Numerically Stable Methods for Quadratic Programming,” Mathematical Programming14: 349–372.
77. Gene Golub, Virginia Klema, and Stephen C. Peters (1980), “Rules and Software for Detecting Rank Degeneracy,” Journal of Econometrics12: 41–8.
78. Gene H. Golub and Charles van Loan (1984), Matrix Computations. Baltimore: Johns Hopkins University Press.
79. James H. Goodnight (1979), “A Tutorial on the SWEEP Operator,” American Statistician33: 149–58.
80. Peter J. Huber (1964), “Robust Estimation of a Location Parameter”, Annals of Mathematical Statistics35: 73–101.
81. Jinseog Kim, Yuwon Kim, and Yongdai Kim (2008), “A Gradient-Based Optimization Algorithm for LASSO,” Journal of Computational and Graphical Statistics17: 994–1009.
82. Charles L. Lawson and Richard J. Hanson (1974), Solving Least Squares Problems. Englewood Cliffs, NJ: Prentice-Hall.
83. James W. Longley (1967), “An Appraisal of Least Squares Programs for the Electronic Computer for the Point of View of the User,” Journal of the American Statistical Association62: 819–41.
84. Allen McIntosh (1982), Fitting Linear Models: An Application of Conjugate Gradient Algorithms. New York: Springer-Verlag.
85. Raymond H. Myers (1989), Classical and Modern Regression with Applications, 2nd ed. Boston: PWS-Kent.
86. Michael R. Osborne, Brett Presnell, and Berwin A. Turlach (2000), “On the LASSO and Its Dual,” Journal of Computational and Graphical Statistics9: 319–337.
87. Stephen Portnoy and Roger Koenker (1997), “The Gaussian Hare and the Laplacian Tortoise: Computability of Square-Error versus Absolute-error Estimators,” Statistical Science, 12: 279–300.
88. M. Schatzoff, R. Tsao, and S. Feinberg (1968), “Efficient Calculation of All Possible Regressions,” Technometrics10: 769–79.
89. Shayle R. Searle (1973), Linear Models. New York: Wiley.
90. George W. Snedecor and William G. Cochran (1967), Statistical Methods, 6th ed. Ames: Iowa State University Press.
91. R. G. D. Steel and J. H. Torrie (1980), Principles and Procedures of Statistics, 2nd ed. New York: McGraw-Hill.
92. G.W. Stewart (1973), Introduction to Matrix Computations. New York: Academic Press.
93. G. W. Stewart (1976), “The Economic Storage of Plane Rotations,” Numerische Mathematik25: 137–8.
94. Robert Tibshirani (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society58: 267–288.
95. Paul F. Velleman and Roy E.Welsch (1981), “Efficient Computing of Regression Diagnostics,” American Statistician35: 234–42.
96. Roy H. Wampler (1980), “Test Procedures and Test Problems for Least Squares Algorithms,” Journal of Econometrics12: 3–22.
97. E. Anderson, Z. Bai, C. Bishof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorenson (1995), LAPACK Users’Guide. Philadelphia: SIAM.
98. T. F. Chan (1982), “An Improved Algorithm for Computing the Singular Value Decomposition,” ACM Transactions on Mathematical Software8: 72–88.
99. Gene H. Golub and Charles van Loan (1989), Matrix Computations, 2nd ed. Baltimore: Johns Hopkins University Press.
100. W. J. Harrod and R. J. Plemmons (1984), “Comparison of Some Direct Methods for Computing Stationary Distributions of Markov Chains,” SIAM Journal of Scientific and Statistical Computing5: 453–68.
101. Alan Jennings (1977), Matrix Computation for Engineers and Scientists. New York:Wiley.
102. Charles L. Lawson and Richard J. Hanson (1974), Solving Least Squares Problems. Englewood Cliffs, NJ: Prentice-Hall.
103. K. V. Mardia, J. T. Kent, and J. M. Bibby (1979), Multivariate Analysis. London: Academic Press.
104. B. N. Parlett and W. G. Poole (1973), “A Geometric Theory for the QR, LU and Power Iterations,” SIAM Journal of Numerical Analysis10: 389–412.
105. G.W. Stewart (1973), Introduction to Matrix Computations. New York: Academic Press.
106. William J. Stewart (1978), “A Comparison of Numerical Techniques in Markov Modeling,” Communications of the ACM21: 144–52.
107. William J. Stewart (Ed.) (1991), Numerical Solution of Markov Chains. New York: Marcel Dekker.
108. William J. Stewart and Alan Jennings (1981), “A Simultaneous Iteration Method for Real Matrices,” ACM Transactions on Mathematical Software7: 184–98.
109. J. H. Wilkinson (1965), The Algebraic Eigenvalue Problem. London: Oxford University Press.
110. Milton Abramowitz and Irene A. Stegun (Eds.) (1970), Handbook of Mathematical Functions. New York: Dover.
111. J. H. Ahlberg, E. N. Nilsson, and J. L. Walsh (1967), The Theory of Splines and Their Applications. New York: Academic Press.
112. B. J. R. Bailey (1981), “Alternatives to Hastings’ Approximation to the Inverse of the Normal Cumulative Distribution Function,” Applied Statistics30: 275–6.
113. Douglas M. Bates, Mary J. Lindstrom, Grace Wahba, and Brian S. Yandell (1987), “GCVPACK: Routines for Generalized Cross Validation,” Communications in Statistics B16: 263–97.
114. Peter Bloomfield (1976), Fourier Analysis of Time Series: An Introduction. New York: Wiley.
115. N. E. Bosten and E. L. Battiste (1973), “Remark on Algorithm 179, Incomplete Beta Ratio,” Communications of the ACM17: 156–7.
116. W. J. Cody, W. Fraser, and J. F. Hart (1968), “Rational Chebyshev Approximation Using Linear Equations,” Numerische Mathematik12: 242–51.
117. William J. Cody and William Waite (1980), Software Manual for the Elementary Functions. Englewood Cliffs, NJ: Prentice-Hall.
118. P. Craven and G. Wahba (1979), “Smoothing Noisy Data with Spline Functions,” Numerische Mathematik31: 377–403.
119. Germund Dahlquist and Ake Bjorck (1974), Numerical Methods(trans. by N. Anderson). Englewood Cliffs, NJ: Prentice-Hall.
120. Philip J. Davis (1975), Interpolation and Approximation. New York: Dover.
121. Carl De Boor (1978), A Practical Guide to Splines. New York: Springer-Verlag.
122. Armido R. DiDonato and Alfred H. Morris, Jr. (1992), “Algorithm 708: Significant Digit Computation of the Incomplete Beta Ratio,” ACM Transactions on Mathematical Software18: 360–73.
123. D. R. Divgi (1979), “Calculation of Univariate and Bivariate Normal Probability Functions,” Annals of Statistics7: 903–10.
124. Zvi Dresner (1978), “Computation of the Bivariate Normal Integral,” Mathematics of Computation32: 277–9.
125. Zvi Dresner and G. O. Wesolowsky (1990), “On the Computation of the Bivariate Normal Integral,” Journal of Statistical Computation and Simulation35: 101–7.
126. E. S. Eppright, H. M. Fox, B.A. Fryer, G. H. Lamkin, V. M. Vivian, and E. S. Fuller (1972), “Nutrition of Infants and Preschool Children in the North Central Region of the United States of America,” World Review of Nutrition and Dietetics14: 269–332.
127. R. L. Eubank (1988), Spline Smoothing and Nonparametric Regression. New York: Marcel Dekker.
128. C. T. Fike (1968), Computer Evaluation of Mathematical Functions. Englewood Cliffs, NJ: Prentice-Hall.
129. Wayne A. Fuller (1996), Introduction to Statistical Time Series, 2nd ed. New York: Wiley.
130. W. Gautschi (1979), “A Computational Procedure for Incomplete Gamma Functions,” ACM Transactions on Mathematical Software5: 466–81.
131. C. A. Hall and W. W. Meyer (1976), “Optimal Error Bounds for Cubic Spline Interpolation,” Journal of Approximation Theory16: 105–22.
132. John F. Hart, E.W. Cheney, Charles L. Lawson, Hans J. Maehly, Charles K. Mesztenyi, John R. Rice, Henry G. Thatcher, Jr., and Christoph Witzgall (1968), Computer Approximations. New York: Wiley; reprinted 1978 by Kreiger (Malabar, FL).
133. C. Hastings (1955), Approximations for Digital Computers. Princeton, NJ: Princeton University Press.
134. M. F. Hutchinson (1986), “Algorithm 642: A Fast Procedure for Calculating Minimum Cross-Validation Cubic Smoothing Splines,” ACM Transactions on Mathematical Software12: 150–3.
135. Robert A. Lew (1981), “An Approximation to the Cumulative Normal Distribution with Simple Coefficients,” Applied Statistics30: 299–301.
136. Robert F. Ling (1978), “A Study of the Accuracy of Some Approximation for t, chi-square, and F Tail Probabilities,” Journal of the American Statistical Association73: 274–83.
137. K. L. Majumder and G. P. Bhattacharjee (1973), “Algorithm AS63: The Incomplete Beta Integral,” Applied Statistics22: 409–11.
138. John F. Monahan (1981), “Approximating the Log of the Normal Cumulative,” in W. F. Eddy (Ed.), Computer Science and Statistics: Proceedings of the Thirteenth Annual Symposium on the Interface, pp. 304–7. New York: Springer-Verlag.
139. John F. Monahan and Leonard A. Stefanski (1992), “Normal Scale Mixture Approximations to F ∗(z) and Computation of the Logistic–Normal Integral,” in N. Balakrishnan (Ed.), Handbook of the Logistic Distribution, pp. 529–40. New York: Marcel Dekker.
140. R. E. Odeh and J. O. Evans (1974), “Algorithm AS70: The Percentile Points of the Normal Distribution,” Applied Statistics23: 96–7.
141. Dale J. Poirier (1973), “Piecewise Regression Using Cubic Splines,” Journal of the American Statistical Association68: 515–24.
142. Christian H. Reinsch (1967), “Smoothing by Spline Functions,” Numerische Mathematik10: 177–83.
143. ChristianH. Reinsch (1971), “Smoothing by Spline Functions II,” Numerische Mathematik16: 451–4.
144. Harold Ruben (1961), “Probability Contents of Regions under Spherical Normal Distributions III: The Bivariate Normal Integral,” Annals of Mathematical Statistics32: 171–86.
145. David Ruppert, M. P. Wand, and R. J. Carroll (2003), Semiparametric Regression. New York: Cambridge University Press.
146. B. W. Silverman (1985), “Some Aspects of the Spline Smoothing Approach to Nonparametric Regression Curve Fitting,” Journal of the Royal Statistical Society B47: 1–52.
147. H. E. Soper (1921), “The Numerical Evaluation of the Incomplete Beta-Function,” in Tracts for Computers(no. 7). Cambridge University Press.
148. G. Szego (1959), Orthogonal Polynomials. Providence, RI: American Mathematical Society.
149. John D. Vedder (1993), “An Invertible Approximation to the Normal Distribution Function,” Computational Statistics and Data Analysis16: 119–23.
150. Christopher H. Bodily (2002), “Numerical Differentiation Using Statistical Design,” unpublished Ph.D. thesis, North Carolina State University.
151. R. P. Brent (1973), Algorithms for Minimization without Derivatives. Englewood Cliffs, NJ: Prentice-Hall.
152. D. R. Cox (1970), Analysis of Binary Data. London: Methuen.
153. J. E. Dennis, Jr. (1984), “A User’s Guide to Nonlinear Optimization Algorithms,” Proceedings of the IEEE72: 1765–76.
154. J. E. Dennis, Jr., and R. B. Schnabel (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Englewood Cliffs, NJ: Prentice-Hall.
155. M. Dowell and P. Jarratt (1971), “A Modified Regula Falsi Method for Computing the Root of an Equation,” BIT11: 168–74.
156. D.M. Gay (1983), “Algorithm 611: Subroutines for Unconstrained Minimization Using a Model/Trust Region Approach,” ACM Transactions on Mathematical Software9: 503–24.
157. P. E. Gill, W. Murray, and M. H. Wright (1981), Practical Optimization. London: Academic Press.
158. D. Goldfarb (1976), “Factorized Variable Metric Methods for Unconstrained Optimization,” Mathematics of Computation30: 796–811.
159. Andreas Griewank and Andrea Walther (2008), Evaluating Derivatives: Principles and Techniques for Algorithmic Differentiation. 2nd edition, Philadelphia: SIAM.
160. C. T. Kelley (1999), Iterative Methods for Optimization. Philadelphia: SIAM.
161. D.G. Luenberger (1984), Linear and Nonlinear Programming, 2nd ed. Reading, MA: Addison-Wesley.
162. B. D. McCullough and H. D. Vinod (2003), “Verifying the Solution from a Nonlinear Solver: A Case Study,” The American Economic Review93: 873–91.
163. J. A. Nelder and R. Mead (1965), “A Simplex Method for Function Minimization,” The Computer Journal7: 308–13.
164. M. J. D. Powell (1970), “A New Algorithm for Unconstrained Optimization,” in J. B. Rosen, O. L. Mangasarian, and K. Ritter (Eds.), Nonlinear Programming, pp. 31–65. New York: Academic Press.
165. H. Rosenbrock (1960), “An Automatic Method for Finding the Greatest or Least Value of a Function,” Computer Journal3: 175–84.
166. W. Spendley, G. R. Hext, and F. R. Himsworth (1962), “Sequential Application of Simplex Designs in Optimization and Evolutionary Operation,” Technometrics4: 441–61.
167. Michael N. Vrahatis (1988), “Solving Systems of Nonlinear Equations Using the Nonzero Value of the Topological Degree,” ACM Transactions on Mathematical Software14: 312–29.
168. D. J. Wilde (1964), Optimum Seeking Methods. Englewood Cliffs, NJ: Prentice-Hall.
169. F. S. Acton (1970), Numerical Methods That Work. New York: Harper & Row.
170. A. Albert and J. A. Anderson (1984), “On the Existence of Maximum Likelihood Estimates in Logistic Regression Models,” Biometrika71: 1–10.
171. Y. Bard (1974), Nonlinear Parameter Estimation. New York: Academic Press.
172. D.M. Bates, D. C. Hamilton, and D. G. Watts (1983), “Calculation of Intrinsic and Parameter-Effects Curvatures for Nonlinear Regression Models,” Communications in Statistics B12: 469–77.
173. D. M. Bates and D. G. Watts (1980), “Relative Curvature Measures of Nonlinearity,” Journal of the Royal Statistical Society B42: 1–25.
174. D. M. Bates and D. G. Watts (1988), Nonlinear Regression Analysis and Its Applications. New York: Wiley.
175. Dennis D. Boos (1992), “On Generalized Score Tests,” American Statistician46: 327–33.
176. D. R. Cox (1970), Analysis of Binary Data. London: Methuen.
177. A. P. Dempster, N. M. Laird, and D. B. Rubin (1977), “Maximum Likelihood from Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society B39: 1–38.
178. J. E. Dennis, Jr., D. M. Gay, and Roy E. Welsch (1981), “An Adaptive Nonlinear Least-Squares Algorithm,” ACM Transactions on Mathematical Software7: 348–83.
179. J. E. Dennis, Jr., and R. B. Schnabel (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Englewood Cliffs, NJ: Prentice-Hall.
180. B. Efron and D. V. Hinkley (1978), “Assessing the Accuracy of the Maximum Likelihood Estimator: Observed versus Expected Fisher Information,” Biometrika65: 457–87.
181. D. J. Finney (1947), “The Estimation from Individual Records of the Relationship Between Dose and Quantal Response,” Biometrika34: 320–34.
182. E. L. Frome (1983), “The Analysis of Rates Using Poisson Regression Models,” Biometrics39: 665–74.
183. W. A. Fuller (1976), Introduction to Statistical Time Series. New York: Wiley.
184. A. R. Gallant (1975), “Nonlinear Regression,” American Statistician29: 73–81.
185. A. R. Gallant (1987), Nonlinear Statistical Models. New York: Wiley.
186. M. D. Hebden (1973), “An Algorithm for Minimization Using Exact Second Derivatives,” Report no. TP515, Atomic Energy Research Establishment, Harwell, U.K.
187. Paul W. Holland and Roy E. Welsch (1977), “Robust Regression Using Iteratively Reweighted Least Squares,” Communications in StatisticsA6: 813–27.
188. R. I. Jennrich and R. H. Moore (1975), “Maximum Likelihood Estimation by Means of Nonlinear Least Squares,” in Proceedings of the Statistical Computing Section, pp. 57–65.Washington, DC: American Statistical Association.
189. R. I. Jennrich and P. F. Sampson (1968), “An Application of Stepwise Regression to Non-Linear Estimation,” Technometrics10: 63–72.
190. L. LeCam (1956), “On the Asymptotic Theory of Estimation and Testing Hypotheses,” in Proceedings of the Third Berkeley Symposium of Mathematical Statistics and Probability, vol. 1, pp. 129–56. Berkeley: University of California Press.
191. L. LeCam (1970), “On the Assumptions Used to Prove Asymptotic Normality of Maximum Likelihood Estimators,” Annals of Mathematical Statistics41: 802–28.
192. L. LeCam and G. Yang (1990), Asymptotics in Statistics: Some Basic Concepts. New York: Springer-Verlag.
193. D. Marquardt (1963), “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” SIAM Journal of Applied Mathematics11: 431–41.
194. P. McCullagh and J. A. Nelder (1992), Generalized Linear Models, 2nd ed. New York: Chapman & Hall.
195. John F. Monahan (1983), “Fully Bayesian Analysis of ARMA Time Series Models,” Journal of Econometrics21: 307–31.
196. Jorge J. Moré (1977), “The Levenberg–Marquardt Algorithm: Implementation and Theory,” in G. A. Watson (Ed.), Numerical Analysis(Lecture Notes in Mathematics, no. 630), pp. 105–16. Berlin: Springer-Verlag.
197. Jorge J. Moré, Burton S. Garbow, and Kenneth E. Hillstrom (1981), “Testing Unconstrained Optimization Software,” ACM Transactions on Mathematical Software7: 17–41.
198. S. A. Murphy and A.W. van der Vaart (2000), “On Profile Likelihood,” Journal of the American Statistical Association95: 449–65.
199. J. Neyman and E. Scott (1948), “Consistent Estimates Based on Partially Consistent Observations,” Econometrica16: 1–32.
200. C. R. Rao (1973), Linear Statistical Inference and Its Applications, 2nd ed. New York: Wiley.
201. Thomas J. Santner and Diane E. Duffy (1986), “A Note on A. Albert and J. A. Anderson’s Conditions for the Existence of Maximum Likelihood Estimates in Logistic Regression Models,” Biometrika73: 755–58.
202. R. J. Serfling (1980), Approximation Theorems and Mathematical Statistics. New York: Wiley.
203. Houston H. Stokes (2004), “On the Advantage of Using Two or More Econometric Software Systems to Solve the Same Problem,” Journal of Economic and Social Measurement29: 307–20.
204. A. Wald (1949), “Note on the Consistency of the Maximum Likelihood Estimate,” Annals of Mathematical Statistics20: 595–601.
205. R. W. M. Wedderburn (1976), “On the Existence and Uniqueness of the Maximum Likelihood Estimates for Certain Generalized Linear Models,” Biometrika63: 27–32.
206. J. Wolfowitz (1949), “On Wald’s Proof of the Consistency of the Maximum Likelihood Estimate,” Annals of Mathematical Statistics20: 601–2.
207. C. F. Jeff Wu (1981), “Asymptotic Theory of Nonlinear Least Squares Estimation,” Annals of Statistics9: 501–13.
208. C. F. JeffWu (1983), “On the Convergence Properties of the EM Algorithm,” Annals of Statistics11: 95–103.
209. Milton Abramowitz and Irene Stegun (Eds.) (1970), Handbook of Mathematical Functions. New York: Dover.
210. D. F. Andrews, P. J. Bickel, F. R. Hampel, P. J. Huber, W. H. Rogers, and J.W. Tukey (1972), Robust Estimates of Location. Princeton, NJ: Princeton University Press.
211. C. Bays and S. D. Durham (1976), “Improving a Poor Random Number Generator,” ACM Transactions on Mathematical Software2: 59–64.
212. Paul Bratley, Bennett L. Fox, and Linus Schrage (1983), A Guide to Simulation. New York: Springer-Verlag.
213. H. S. Bright and R. L. Enison (1979), “Quasi-Random Number Sequences from a Long-Period TLP Generator with Remarks on Application to Cryptography,” Computing Surveys11: 357–70.
214. P. D. Coddington (1994), “Analysis of Random Number Generators Using Monte Carlo Simulation,” International Journal of Modern Physics C5: 547–60.
215. R. Cranley and T. N. L. Patterson (1976), “Randomization of Number Theoretic Methods for Multiple Integration,” SIAM Journal of Numerical Analysis13: 904–14.
216. Philip J. Davis (1975), Interpolation and Approximation. New York: Dover.
217. Philip J. Davis and Philip Rabinowitz (1984), Methods of Numerical Integration, 2nd ed. Orlando, FL: Academic Press.
218. K.-T. Fang and Y. Wang (1994), Number-Theoretic Methods in Statistics. London: Chapman & Hall.
219. A. M. Ferrenberg, D. P. Landau, and Y. J. Wong (1992), “Monte Carlo Simulations: Hidden Errors from ‘Good’ Random Number Generators,” Physical Review Letters69: 3382–4.
220. George S. Fishman and Louis R. Moore (1982), “A Statistical Evaluation of Multiplicative Congruential Generators with Modulus 231−1,” Journal of the American Statistical Association77: 129–36.
221. George S. Fishman and Louis R. Moore (1986), “An Exhaustive Analysis of Multiplicative Congruential Random Number Generators with Modulus 231−1,” SIAM Journal of Scientific and Statistical Computing7: 24–45.
222. Nancy Flournoy and Robert K. Tsutakawa (Eds.) (1991), Statistical Multiple Integration(Contemporary Mathematics Series, vol. 115). Providence, RI: American Mathematical Society.
223. M. Fushimi and S. Tezuka (1983), “The k-Distribution of Generalized Feedback Shift Register Pseudorandom Numbers,” Communications of the ACM26: 516–23.
224. John Geweke (1989), “Bayesian Inference in Econometric Models Using Monte Carlo Integration,” Econometrica57: 1317–39.
225. E. R. Golder (1976), “The Spectral Test for the Evaluation of Congruential Pseudo-random Generators,” Applied Statistics25: 173–80. [Corrections in Volume 25, p. 324 (Golder) and Volume 27, pp. 375–6 (Hoaglin and King).]
226. Gene H. Golub and J. H. Welsch (1969), “Calculation of Gauss Quadrature Rules,” Mathematics of Computation23: 221–30.
227. A. M. Gross (1973), “A Monte Carlo Swindle for Estimators of Location,” Applied Statistics22: 347–53.
228. J. H. Halton and G. B. Smith (1964), “Algorithm 247: Radical-Inverse Quasi-Random Point Sequence,” Communications of the ACM7: 701–2.
229. J. M. Hammersley and D. C. Handscomb (1964), Monte Carlo Methods. London: Methuen.
230. W. Hormann and G. Derflinger (1993), “A Portable Random Number Generator Well Suited for the Rejection Method,” ACM Transactions on Mathematical Software19: 489–95.
231. Loo Keng Hua and Yuan Wang (1981), Applications of Number Theory to Numerical Analysis. New York: Springer-Verlag.
232. Gershon Kedem and S. K. Zaremba (1974), “A Table of Good Lattice Points in Three Dimensions,” Numerische Mathematik23: 175–80.
233. Donald E. Knuth (1997), The Art of Computer Programming(vol. 2: Seminumerical Algorithms), 3rd ed. Reading, MA: Addison-Wesley.
234. V. I. Krylov (1962), Approximate Calculation of Integrals(trans. by A. H. Stroud). New York: Macmillan.
235. L. Kuipers and H. Neiderreiter (1974), Uniform Distribution of Sequences. New York: Wiley.
236. Pierre L’Ecuyer (1988), “Efficient and Portable Random Number Generators,” Communications of the ACM31: 742–9, 774.
237. Pierre L’Ecuyer (1990), “Random Numbers for Simulation,” Communications of the ACM33: 85–97.
238. P. A.W. Lewis, A. S. Goodman, and J. M. Miller (1969), “A Pseudo-random Number Generator for the System/360,” IBM Systems Journal2: 136–46.
239. T. G. Lewis and W. H. Payne (1973), “Generalized Feedback Shift Register Pseudorandom Number Algorithm,” Journal of the Association for Computing Machinery30: 456–68.
240. M. D. MacLaren and G. Marsaglia (1965), “Uniform Random Number Generators,” Journal of the ACM12: 83–9.
241. Dominique Maisonneuve (1972), “Recherche et Utilisation des ‘Bons Treillis.’ Programmation et Resultats Numeriques,” in S. K. Zaremba (Ed.), Applications of Number Theory to Numerical Analysis, pp. 121–201. New York: Academic Press.
242. George Marsaglia (1968), “Random Numbers Fall Mainly in the Planes,” Proceedings of the National Academy of Sciences61: 25–8.
243. George Marsaglia (1972), “The Structure of Linear Congruential Sequences,” in S. K. Zaremba (Ed.), Applications of Number Theory to Numerical Analysis, pp. 249–85. New York: Academic Press.
244. George Marsaglia (1985), “A Current View of Random Number Generators,” in L. Ballard (Ed.), Computer Science and Statistics: Proceedings of the Sixteenth Symposium on the Interface, pp. 3–10. Amsterdam: North-Holland.
245. Makoto Matsumoto and Takuji Nishimura (1998), “Mersenne Twister:A623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator,” ACM Transactions on Modeling and Computer Simulation, 8: 3–30.
246. I. P. Mysovskikh (1980), “The Approximation of Multiple Integrals by using Interpolatory Cubature Formulae,” in R. A. DeVore and K. Scherer (Eds.), Quantitative Approximation, pp. 217–43. New York: Academic Press.
247. Harald Neiderreiter (1978), “Quasi–Monte Carlo Methods and Pseudo-Random Numbers,” Bulletin of the American Mathematical Society84: 957–1041.
248. Harald Neiderreiter (1987), “Statistical Analysis of Generalized Feedback Shift Register Pseudorandom Generators,” SIAM Journal of Scientific and Statistical Computing8: 1035–51.
249. Harald Neiderreiter (1992), Random Number Generation and Quasi–Monte Carlo Methods. Philadelphia: SIAM.
250. Francois Panneton, Pierre L’Ecuyer, and Makoto Matsumoto (2006), “Improved Long-Period Generators Based on Linear Recurrences Modulo 2,” ACM Transactions on Mathematical Software32: 1–16.
251. Stephen K. Park and KeithW. Miller (1988), “Random Number Generators: Good Ones Are Hard to Find,” Communications of the ACM31: 1192–1201.
252. Stephen K. Park, Keith W. Miller, and Paul K. Stockmeyer (1993), “Technical Correspondence,” Communications of the ACM36: 108–10.
253. P. D. Proinov (1988), “Discrepancy and Integration of Continuous Functions,” Journal of Approximation Theory52: 121–31.
254. Daniel A. Relles (1970), “Variance Reduction Techniques for Monte Carlo Sampling from Student Distributions,” Technometrics12: 499–515.
255. Brian D. Ripley (1983), “Computer Generation of Random Variables: ATutorial,” International Statistical Review51: 301–19.
256. Brian D. Ripley (1987), Stochastic Simulation. New York: Wiley.
257. Linus Schrage (1979), “A More Portable Fortran Random Number Generator,” ACM Transactions on Mathematical Software5: 132–8.
258. Gary Simon (1976), “Computer Simulation Swindles, with Applications to Estimates of Location and Dispersion,” Applied Statistics25: 266–74.
259. A. H. Stroud (1971), Approximate Calculation of Multiple Integrals. Englewood Cliffs, NJ: Prentice-Hall.
260. A. H. Stroud and D. H. Secrest (1966), Gaussian Quadrature Formulas. Englewood Cliffs, NJ: Prentice-Hall.
261. William H. Swallow and John F. Monahan (1984), “Monte Carlo Comparison of ANOVA, MIVQUE, REML, and ML Estimators of Variance Components,” Technometrics26: 47–57.
262. R. C. Tausworthe (1965), “Random Numbers Generated by Linear Recurrence Modulo Two,” Mathematics of Computation19: 201–9.
263. Shu Tezuka (1995), Uniform Random Numbers: Theory and Practice. Boston: Kluwer.
264. B. A. Wichmann and J. D. Hill (1982), “Algorithm AS 183: An Efficient and Portable Pseudorandom Number Generator,” Applied Statistics31: 188–90; 33: 123.
265. Alan Agresti, Dennis Wackerly, and James M. Boyett (1979), “Exact Conditional Tests for Cross- Classifications: Approximation of Attained Significance Levels,” Psychometrika44: 75–83.
266. J. H. Ahrens and U. Dieter (1974), “Computer Methods for Sampling from Gamma, Beta, Poisson, and Normal Distributions,” Computing12: 223–46.
267. J. H. Ahrens and U. Dieter (1991), “A Convenient Sampling Method with Bounded Computation Times for Poisson Distributions,” in Peter R. Nelson (Ed.), The Frontiers of Statistical Computation, Simulation and Modeling, pp. 137–49. Columbus, OH: American Sciences Press.
268. M. S. Bartlett (1933), “On the Theory of Statistical Regression,” Proceedings of the Royal Society of Edinburgh53: 260–83.
269. George E. P. Box and Mervin E. Muller (1958), “A Note on the Generation of Random Normal Deviates,” Annals of Mathematical Statistics29: 610–11.
270. Paul Bratley, Bennett L. Fox, and Linus E. Schrage (1983), A Guide to Simulation. Berlin: Springer-Verlag.
271. Morris H. DeGroot (1970), Optimal Statistical Decisions. New York: McGraw-Hill.
272. Luc Devroye (1986), Non-Uniform Random Variate Generation. New York: Springer-Verlag.
273. George Forsythe (1972), “Von Neumann’s Comparison Method for Random Sampling from Normal and Other Distributions,” Mathematics of Computation26: 817–26.
274. Albert J. Kinderman and John F. Monahan (1977), “Computer Generation of Random Variables Using the Ratio of Uniform Deviates,” ACM Transactions on Mathematical Software3: 257–60.
275. Albert J. Kinderman and John F. Monahan (1980), “New Methods for Generating Student’s t and Gamma Variables,” Computing25: 369–77.
276. Albert J. Kinderman, John F. Monahan, and John G. Ramage (1977), “Computer Methods for Sampling from Student’s t Distribution,” Mathematics of Computation31: 1009–18.
277. Donald E. Knuth (1997), The Art of Computer Programming(vol. 2: Seminumerical Algorithms), 3rd ed. Reading, MA: Addison-Wesley.
278. Richard A. Kronmal and ArthurV. Peterson, Jr. (1979), “On the Alias Method for Generating Random Variables from a Discrete Distribution,” American Statistician33: 214–18.
279. Joseph B. Kruskal (1969), “An Extremely Portable Random Number Generator,” Communications of the ACM12: 93–4.
280. J. L. Leva (1992), “A Fast Normal Random Number Generator,” ACM Transactions on Mathematical Software18: 449–53.
281. George Marsaglia (1961), “Generating Exponential Random Variables,” Annals of Mathematical Statistics32: 899–902.
282. George Marsaglia and T. A. Bray (1964), “A Convenient Method for Generating Normal Variables,” SIAM Review6: 260–4.
283. John F. Monahan (1979), “Extensions of von Neumann’s Method for Generating Random Variables,” Mathematics of Computation33: 1065–9.
284. John F. Monahan (1985), “Accuracy in Random Number Generation,” Mathematics of Computation45: 559–68.
285. John F. Monahan (1987), “An Algorithm for Generating Chi Random Variables,” ACM Transactions on Mathematical Software13: 168–72.
286. Henry R. Neave (1973), “On Using the Box–Muller Transformation with Multiplicative Congruential Pseudo-random Number Generators,” Applied Statistics22: 92–7.
287. Shayle R. Searle (1971), Linear Models. New York: Wiley.
288. Masaaki Sibuya (1962), “Exponential and Other Random Variable Generators,” Annals of the Institute of Statistical Mathematics13: 231–7.
289. W. B. Smith and R. R. Hocking (1972), “Algorithm AS 53:Wishart Variate Generator,” Applied Statistics21: 341–5.
290. Ernst Stadlober (1989), “Sampling from Poisson, Binomial and Hypergeometric Distributions: Ratio of Uniforms as a Simple and Fast Alternative,” Mathematisch–Statistische Sektion 303. Forschungsgesellschaft Joanneum, Graz, Austria.
291. Ernst Stadlober (1990), “The Ratio of Uniforms Approach for Generating Discrete Random Variables,” Journal of Computational and Applied Mathematics31: 181–9.
292. Ernst Stadlober (1991), “Binomial Random Variate Generation: A Method Based on Ratio of Uniforms,” in Peter R. Nelson (Ed.), The Frontiers of Statistical Computation, Simulation and Modeling, pp. 93–112. Columbus, OH: American Sciences Press.
293. Jeffrey S. Vitter (1987), “An Efficient Algorithm for Sequential Random Sampling,” ACM Transactions on Mathematical Software13: 58–67.
294. John von Neumann (1951), “Various Techniques in Connection with Random Digits,” in Monte Carlo Method(AMS 12), pp. 36–8.Washington, DC: National Bureau of Standards.
295. Alastair J. Walker (1977), “An Efficient Method for Generating Random Variables with General Distributions,” ACM Transactions on Mathematical Software3: 253–6.
296. Milton Abramowitz and Irene A. Stegun (Eds.) (1970), Handbook of Mathematical Functions. New York: Dover.
297. Dennis D. Boos (1984), “Using Extreme Value Theory to Estimate Large Percentiles,” Technometrics26: 33–9.
298. N. N. Cencov (1962), “Evaluation of an Unknown Distribution Density from Observations,” Soviet Mathematics3: 1559–62.
299. William G. Cochran (1954), “Some Methods for Strengthening the Common χ2 Tests,” Biometrics10: 417–51.
300. R. Cranley and T. N. L. Patterson (1976), “Randomization of Number Theoretic Methods for Multiple Integration,” SIAM Journal on Numerical Analysis13: 904–14.
301. E. C. Fieller (1954), “Some Problems in Interval Estimation,” Journal of the Royal Statistical Society B16: 175–85.
302. Alan Genz and John Monahan (1998), “Stochastic Integration Rules for Infinite Regions,” SIAM Journal of Scientific Computation19: 426–39.
303. John Geweke (1989), “Bayesian Inference in Econometric Models Using Monte Carlo Integration,” Econometrica57: 1317–39.
304. E. Haeusler and J. L. Teugels (1985), “On Asymptotic Normality of Hill’s Estimator for the Exponent of Regular Variation,” Annals of Statistics13: 743–56.
305. P. Hall (1982), “On Some Simple Estimates of an Exponent of Regular Variation,” Journal of the Royal Statistical Society B44: 37–42.
306. Richard M. Heiberger (1978), “Algorithm AS127: Generation of Random Orthogonal Matrices,” Applied Statistics27: 199–206.
307. Tim Hesterberg (1995), “Weighted Average Importance Sampling and Defensive Mixture Distributions,” Technometrics37: 185–94.
308. B.W. Hill (1975), “A Simple General Approach to Inference about the Tail of a Distribution,” Annals of Statistics3: 1163–74.
309. H. B. Mann and A. Wald (1942), “On the Choice of the Number of Class Intervals in the Application of the Chi-Square Test,” Annals of Mathematical Statistics13: 306–17.
310. J. F. Monahan (1993), “Testing the Behavior of Importance Sampling Weights,” Computing Science and Statistics24: 112–17.
311. John Monahan and Alan Genz (1997), “Spherical-Radial Integration Rules for Bayesian Computation,” Journal of the American Statistical Association92: 664–74.
312. David S. Moore (1986), “Tests of Chi-Squared Type,” in R. B. D’Agostino and M. A. Stephens (Eds.), Goodness-of-Fit Techniques, pp. 63–95. New York: Marcel Dekker.
313. J. T. Roscoe and J. A. Byars (1971), “An Investigation of the Restraints with Respect to Sample Size Commonly Imposed on the Use of Chi–Square Statistic,” Journal of the American Statistical Association66: 755–9.
314. A. F. Siegel and F. O’Brien (1985), “Unbiased Monte Carlo Integration Methods with Exactness for Low Order Polynomials,” SIAM Journal on Scientific and Statistical Computing6: 169–81.
315. B.W. Silverman (1986), Density Estimation for Statistics and Data Analysis. London: Chapman & Hall.
316. N. V. Smirnov (1939), “On the Estimation of the Discrepancy between Empirical Curves of Distribution for Two Independent Samples” (in Russian), Bulletin of Moscow University2: 3–16.
317. Michael A. Stephens (1970), “Use of the Kolmogorov–Smirnov, Cramer–von Mises and Related Statistics without Extensive Tables,” Journal of the Royal Statistical Society B32: 115–22.
318. Michael A. Stephens (1986), “Tests Based on EDF Statistics,” in R. B. D’Agostino and M. A. Stephens (Eds.), Goodness-of-Fit Techniques, pp. 97–193. New York: Marcel Dekker.
319. G.W. Stewart (1980), “The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimation,” SIAM Journal on Numerical Analysis17: 403–9.
320. Martin A. Tanner and Ronald A. Thisted (1982), “Remark ASR42. A Remark on AS127. Generation of Random Orthogonal Matrices,” Applied Statistics31: 190–92.
321. Richard A. Tapia and James R. Thompson (1978), Nonparametric Probability Density Estimation. Baltimore: Johns Hopkins University Press.
322. Luke Tierney and Joseph B. Kadane (1986), “Accurate Approximations for Posterior Moments and Marginal Densities,” Journal of the American Statistical Association81: 82–6.
323. Luke Tierney, Robert E. Kass, and Joseph B. Kadane (1989), “Fully Exponential Laplace Approximations to Expectations and Variances of Non positive Functions,” Journal of the American Statistical Association84: 710–16.
324. Grace Wahba (1975), “Interpolating Spline Methods for Density Estimation I: Equi-Spaced Knots,” Annals of Statistics3: 30–48.
325. Geoffrey S. Watson (1983), Statistics on Spheres. New York: Wiley.
326. I. Weissman (1978), “Estimation of Parameters and Large Quantiles Based on the k Largest Observations,” Journal of the American Statistical Association73: 812–15
327. T.W. Anderson (1971), The Statistical Analysis of Time Series. New York: Wiley.
328. George E. P. Box and George C. Tiao (1973), Bayesian Inference in Statistical Analysis. Reading, MA: Addison-Wesley.
329. Paul Bratley, Bennett L. Fox, and Linus Schrage (1983), A Guide to Simulation. New York: Springer-Verlag.
330. K. A. Brownlee (1965), Statistical Theory and Methodology, 2nd ed. New York: Wiley.
331. George Casella and Edward I. George (1992), “Explaining the Gibbs Sampler,” American Statistician46: 167–74.
332. K. S. Chan and C. J. Geyer (1994), Discussion of “Markov Chains for Exploring Posterior Distributions” (by L. Tierney), Annals of Statistics22: 1747–58.
333. Siddhartha Chib and Edward Greenberg (1995), “Understanding the Metropolis–Hastings Algorithm,” American Statistician49: 327–35.
334. Mary Kathryn Cowles and Bradley P. Carlin (1996), “Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review,” Journal of the American Statistical Association91: 883–904.
335. P. Dellaportas and A. F. M. Smith (1993), “Bayesian Inference for Generalized Linear and Proportional Hazards Models via Gibbs Sampling,” Applied Statistics42: 443–59.
336. Luc Devroye (1984), “A Simple Algorithm for Generating Random Variates with a Log-Concave Density,” Computing33: 247–57.
337. Luc Devroye (1986), Non-Uniform Random Variate Generation. New York: Springer-Verlag.
338. R. C. Elston and J. F. Grizzle (1962), “Estimation of Time Response Curves and Their Confidence Bands,” Biometrics18: 148–59.
339. Wayne A. Fuller (1996), Introduction to Statistical Time Series, 2nd ed. New York:Wiley.
340. Alan E. Gelfand, Susan E. Hills, Amy Racine-Poon, and Adrian F. M. Smith (1990), “Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling,” Journal of the American Statistical Association85: 973–85.
341. Andrew Gelman and Donald B. Rubin (1992a), “A Single Sequence from the Gibbs Sampler Gives a False Sense of Security,” in J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith (Eds.), Bayesian Statistics4, pp. 625–31. Oxford, U.K.: Oxford University Press.
342. Andrew Gelman and Donald B. Rubin (1992b), “Inference from Iterative Simulation Using Multiple Sequences,” Statistical Science7: 457–511.
343. E. I. George, U. E. Makov, and A. F. M. Smith (1993), “Conjugate Likelihood Distributions,” Scandinavian Journal of Statistics20: 147–56.
344. J. Geweke (1992), “Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments,” in J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith (Eds.), Bayesian Statistics4, pp. 169–93. Oxford, U.K.: Oxford University Press.
345. Charles J. Geyer (1992), “Practical Markov Chain Monte Carlo,” Statistical Science7: 473–511.
346. W. R. Gilks (1992), “Derivative-Free Adaptive Rejection Sampling for Gibbs Sampling,” in J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith (Eds.), Bayesian Statistics4, pp. 641–9. Oxford, U.K.: Oxford University Press.
347. W. R. Gilks, N. G. Best, and K. K. C. Tan (1995), “Adaptive Rejection Metropolis Sampling within Gibbs Sampling,” Applied Statistics44: 455–72.
348. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter (Eds.) (1996), Markov Chain Monte Carlo in Practice. London: Chapman & Hall.
349. W. R. Gilks and P. Wild (1992), “Adaptive Rejection Sampling for Gibbs Sampling,” Applied Statistics41: 337–48.
350. W. K. Hastings (1970), “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” Biometrika57: 97–109.
351. P. Heidelberger and P. D. Welch (1983), “Simulation Run Length Control in the Presence of an Initial Transient,” Operations Research31: 1109–44.
352. James P. Hobert and George Casella (1996), “The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Models,” Journal of the American Statistical Association91: 1461–73.
353. Robert E. Kass, Bradley P. Carlin, Andrew Gelman, and Radford M. Neal (1998), “Markov Chain Monte Carlo in Practice: A Roundtable Discussion,” American Statistician52: 93–100.
354. Josef Leydold (2000), “Automatic Sampling with the Ratio-of-Uniforms Method,” ACM Transactions on Mathematical Software26: 78–98.
355. Steven N. MacEachern and L. Mark Berliner (1994), “Subsampling the Gibbs Sampler,” American Statistician48: 188–90.
356. N. Metropolis, A.W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller (1953), “Equations of State Calculations by Fast Computing Machines,” Journal of Chemical Physics21: 1087–92.
357. S. P. Meyn and R. L. Tweedie (1993), Markov Chains and Stochastic Stability. New York: Springer.
358. A. E. Raftery and S. Lewis (1992), “How Many Iterations in the Gibbs Sampler?” in J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith (Eds.), Bayesian Statistics4, pp. 763–73. Oxford, U.K.: Oxford University Press.
359. Brian D. Ripley (1987), Stochastic Simulation. New York: Wiley.
360. Gareth O. Roberts and Nicholas G. Polson (1994), “On the Geometric Convergence of the Gibbs Sampler,” Journal of the Royal Statistical Society B56: 377–84.
361. Bruce Schmeiser (1990), “Simulation Experiments,” in D. P. Heyman and M. J. Sobel (Eds.), Handbooks in Operations Research and Management Science(vol. 2: Stochastic Models), pp. 295–330. Amsterdam: North-Holland.
362. David Spiegelhalter, Andrew Thomas, Nicky Best, and Wally Gilks (1996), BUGS: Bayesian Inference Using Gibbs Sampling. Cambridge, U. K.: Cambridge Medical Research Council Biostatistics Unit.
363. M. A. Tanner and W. H. Wong (1987), “The Calculation of Posterior Distributions by Data Augmentation,” Journal of the American Statistical Association82: 528–49.
364. Luke Tierney (1994), “Markov Chains for Exploring Posterior Distributions” (with discussion), Annals of Statistics22: 1701–62.
365. Luke Tierney (1995), “Introduction to General State-Space Markov Chain Theory,” in W. R. Gilks, S. Richardson, and D. J. Spiegelhalter (Eds.), Markov Chain Monte Carlo in Practice. London: Chapman & Hall.
366. Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman (1974), The Design and Analysis of Computer Algorithms. Reading, MA: Addison-Wesley.
367. Jenny Baglivo, Donald Olivier, and Marcello Pagano (1992), “Methods for Exact Goodness-of-Fit Tests,” Journal of the American Statistical Association87: 464–9.
368. L. I. Bluestein (1970), “A Linear Filtering Approach to the Computation of the Discrete Fourier Transform,” IEEE Transactions on Audio and Electroacoustics18: 451–5.
369. Harald Bohman (1975), “Numerical Inversions of Characteristic Functions,” Scandinavian Actuarial Journal, pp. 121–4.
370. J. Boothroyd (1967), “Algorithm 29: Permutation of the Elements of a Vector,” Computer Journal10: 311.
371. J.W. Cooley, P. A. Lewis, and P. D. Welch (1967), “Historical Notes on the Fast Fourier Transform,” IEEE Transactions on Audio and Electroacoustics15: 76–9.
372. J.W. Cooley and J.W. Tukey (1965), “An Algorithm for the Machine Calculation of Complex Fourier Series,” Mathematics of Computation19: 297–301.
373. D. R. Cox and D. V. Hinkley (1974), Theoretical Statistics. London: Chapman & Hall.
374. F. N. David and D. E. Barton (1962), Combinatorial Chance. New York: Hafner.
375. R. B. Davies (1975), “Numerical Inversion of a Characteristic Function,” Biometrika60: 415–17.
376. Robert B. Davies (1980), “ASS 155: The Distribution of a Linear Combination of Chi-Squared Random Variables,” Applied Statistics29: 323–33.
377. I. J. Good, T. N. Gover, and G. J. Mitchell (1970), “Exact Distribution for χ2 and for the Likelihood-Ratio Statistic for the Equiprobable Multinomial Distribution,” Journal of the American Statistical Association65: 267–83.
378. C. A. R. Hoare (1961), “Algorithm 63 (PARTITION) and Algorithm 65 (FIND),” Communications of the ACM4: 321–2.
379. J. L. Hodges and E. L. Lehmann (1963), “Estimates of Location Based on Rank Tests,” Annals of Mathematical Statistics34: 598–611.
380. J. P. Imhof (1961), “Computing the Distribution of Quadratic Forms in NormalVariables,” Biometrika48: 419–26.
381. D. B. Johnson and S. D. Kashdan (1978), “Lower Bounds for Selection in X + Y and Other Multisets,” Journal of the ACM25: 556–70.
382. Gary D. Knott (1974), “A Numbering System for Combinations,” Communications of the ACM17: 45–6.
383. Donald E. Knuth (1997), The Art of Computer Programming(vol. 2: Seminumerical Algorithms), 3rd ed. Reading, MA: Addison-Wesley.
384. Donald E. Knuth (1998), The Art of Computer Programming(vol. 3: Sorting and Searching), 2nd ed. Reading, MA: Addison-Wesley.
385. Lu, Zeng-Hua and Maxwell L. King (2002), “Improving the Numerical Technique for Computing the Accumulated Distribution of a Quadratic Form in Normal Variables,” Econometric Reviews21: 149–65.
386. J.W. McKean and T. A. Ryan (1977), “Algorithm 516: An Algorithm for Obtaining Confidence Intervals and Point Estimates Based on Rank in a Two-Sample Location Problem,” ACM Transactions on Mathematical Software3: 183–5.
387. Cyrus R. Mehta and Nitin R. Patel (1986), “FEXACT: A Fortran Subroutine for Fisher’s Exact Test on Unordered r ×c Contingency Tables,” ACM Transactions on Mathematical Software12: 154–61.
388. John F. Monahan (1984), “Fast Computation of the Hodges–Lehmann Location Estimator,” ACM Transactions on Mathematical Software10: 265–70.
389. John F. Monahan (1987), “An Alternative Method for Computing Overflow Probabilities,” Communications in Statistics A16: 3355–7.
390. A. Nijenhius and H. S. Wilf (1978), Combinatorial Algorithms. New York: Academic Press.
391. Marcello Pagano and David Tritchler (1983), “On Obtaining Permutation Distributions in Polynomial Time,” Journal of the American Statistical Association78: 435–40.
392. L. R. Rabiner, R. W. Schafer, and C. M. Rader (1969), “The Chirp-z Transform Algorithm and Its Applications,” Bell System Technical Journal48: 1249–92.
393. M. V. Ramakrishna (1987), “Computing the Probability of Hash Table/Urn Overflow,” Communications in Statistics A16: 3343–53.
394. Ian Robinson and Simon Sheather (1988), “Fast Computation of the Hodges–Lehmann Estimator and Its Associated Confidence Limits,” American Statistical Association Proceedings of the Statistical Computing Section, pp. 187–91.
395. Mok-Kong Shen (1963), “Algorithm 202: Generation of Permutations in Lexicographical Order,” Communications of the ACM6: 517.
396. B.W. Silverman (1982), “Kernel Density Estimation Using the Fast Fourier Transform,” Applied Statistics31: 93–7.
397. R. C. Singleton (1969), “An Algorithm for Computing the Mixed-Radix Fast Fourier Transform,” IEEE Transactions on Audio and Electroacoustics17: 93–103.
398. Cathie Spino and Marcello Pagano (1991), “Efficient Calculation of the Permutation Distribution of Trimmed Means,” Journal of the American Statistical Association86: 729–37.
399. David Tritchler (1984a), “On Inverting Permutation Tests,” Journal of the American Statistical Association79: 200–7.
400. David Tritchler (1984b), “An Algorithm for Exact Logistic Regression,” Journal of the American Statistical Association79: 709–11.
401. Mark B. Wells (1961), “Generation of Permutations by Transposition,” Mathematics of Computation15: 192–5.