Saddlepoint approximations with applications

Saddlepoint Approximations with Applications

Volumn , Issue , 2007, Pages 1-564

  Butler, Ronald W ^a  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84925105968     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511619083     Document Type: Book

References (292)

1. Aalen, O.O. (1995) Phase type distributions in survival analysis. Scandinavian Journal of Statistics22, 447-463.
2. Abramowitz, M. and Stegun, I.A. (1972)Handbook of Mathematical Functions.Ninth edition. New York: Dover.
3. Agresti, A. (1992) A survey of exact inference for contingency tables. Statistical Science7, 131-153.
4. Aitchison, J. (1986)The Statistical Analysis of Compositional Data.London: Chapman and Hall.
5. Anderson, T.W. (1958)An Introduction to Multivariate Statistical Analysis.New York: Wiley.
6. Anderson, T.W. (1971)The Statistical Analysis of Time Series.New York: Wiley.
7. Anderson, T.W. (1984)An Introduction to Multivariate Statistical Analysis.Second edition. New York: Wiley.
8. Anderson, T.W. (2003)An Introduction to Multivariate Statistical Analysis.Third edition. New York: Wiley.
9. Aroian, L.A. (1939) A study of Fisher's zdistribution and the related Fdistribution, Annals of Mathematical Statistics12, 429-448.
10. Atkinson, A.C. (1982) The simulation of generalized inverse Gaussian and generalized hyperbolic random variables. SIAM Journal on Scientific Computing3, 502-515.
11. Barlow, R.E. and Proschan, F. (1965)Mathematical Theory of Reliability.New York: Wiley.
12. Barndorff-Nielsen, O.E. (1978)Information and Exponential Families in Statistical Theory.New York: Wiley.
13. Barndorff-Nielsen, O.E. (1980) Conditionality resolutions. Biometrika67, 293-310.
14. Barndorff-Nielsen, O.E. (1982) “Exponential Families” entry in the Encyclopedia of Statistical Science, ed. N. L. Johnson and S. Kotz. New York: Wiley.
15. Barndorff-Nielsen, O.E. (1983) On a formula for the conditional distribution of the maximum likelihood estimator. Biometrika70, 343-365.
16. Barndorff-Nielsen, O.E. (1986) Inference on full and partial parameters based on standardized signed log likelihood ratio. Biometrika73, 307-322.
17. Barndorff-Nielsen, O.E. (1988) Comment on Reid (1988). Statistical Science3, 228-229.
18. Barndorff-Nielsen, O.E. (1990) Approximate interval probabilities. Journal of the Royal Statistical Society series B52, 485-499.
19. Barndorff-Nielsen, O.E. (1991) Modified signed log likelihood ratio. Biometrika78, 557-563.
20. Barndorff-Nielsen, O.E. and Cox, D.R. (1979) Edgeworth and saddlepoint approximations with statistical applications (with sDiscussion)Journal of the Royal Statistical Society series B41, 279-312.
21. Barndorff-Nielsen, O.E. and Cox, D.R. (1984) Bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator. Journal of the Royal Statistical Society series B46, 483-495.
22. Barndorff-Nielsen, O.E. and Cox, D.R. (1989)Asymptotic Techniques for Use in Statistics.New York: Chapman and Hall.
23. Barndorff-Nielsen, O.E. and Cox, D.R. (1994)Inference and Asymptotics.New York: Chapman and Hall.
24. Barndorff-Nielsen, O.E. and Hall, P. (1988) On the level-error after Bartlett adjustment of the likelihood ratio statistic. Biometrika75, 374-378.
25. Barndorff-Nielsen, O.E. and Wood, A.T.A. (1998) On large deviations and choice of ancillary for p* and r*. Bernoulli4, 35-63.
26. Bartlett, M.S. (1937) Properties of sufficiency and statistical tests. Proceedings of the Royal Society A160, 268-282.
27. Bartlett, M.S. (1938) The characteristic function of a conditional statistic. Journal of London Mathematical Society13, 62-67.
28. Bedrick, E.J. and Hill, J.R. (1992) An empirical assessment of saddlepoint approximations for testing a logistic regression parameter. Biometrics48, 529-544.
29. Bellio, R. (2003) Likelihood methods for controlled calibration. Scandinavian Journal of Statistics30, 339-353.
30. Bellio, R. and Brazzale, A.R. (1999) Higher-order likelihood-based inference in non-linear regression. in Proceedings of the 14th International Workshop on Statistical Modelling, ed. H. Friedl, A. Berghold, and G. Kauermann, pp. 440-443. Technical University, Graz.
31. Bellio, R. and Brazzale, A.R. (2003) Higher-order asymptotics unleashed: software design for nonlinear heteroscedastic models. Journal of Computational and Graphical Statistics12, 682-697.
32. Bellio, R., Jensen, J.E., and Seiden, P. (2000) Applications of likelihood asymptotics for nonlinear regressions in herbicide bioassays. Biometrics56, 1204-1212.
33. Berger, J.O. (1985)Statistical Decision Theory and Bayesian Analysis.New York: Springer-Verlag.
34. Berger, J.O. and Wolpert, R.L. (1988)The Likelihood Principle, Second edition. Hayward, CA: Institute of Mathematical Statistics.
35. Birnbaum, A. (1962) On the foundations of statistical inference (with discussion). Journal of the American Statistical Association57, 269-306.
36. Bj0rnstad, J.F. (1996) On the generalization of the likelihood function and the likelihood principle. Journal of the American Statistical Association91, 791-806.
37. Blssild, P. and Jensen, J.L. (1985) Saddlepoint formulas for reproductive exponential families. Scandinavian Journal of Statistics12, 193-202.
38. Booth, J.G. (1994) A note on the accuracy of two saddlepoint tail approximations. Proceedings of the Section on Physical and Engineering Sciences56-58. Alexandria, VA: American Statistical Association.
39. Booth, J.G. and Butler, R.W. (1990) Randomization distributions and saddlepoint approximations in generalized linear models. Biometrika77, 787-796.
40. Booth, J.G. and Butler, R.W. (1998). Discussion of “Approximately exact inference for common odds ratio in several 2 tables.”Journal of the American Statistical Association93, 1310-1313.
41. Booth, J.G., Butler, R.W., Huzurbazar, S. and Wood, A.T.A. (1995) Saddlepoint approximations for p-values of some tests of covariance matrices. Journal of Statistical Computation and Simulation53, 165-180.
42. Booth, J.G. and Presnell, B. (1998) Allocation of Monte Carlo resources for the iterated bootstrap. Journal of Computational and Graphical Statistics7, 92-112.
43. Box, G.E.P. (1949) A general distribution theory for a class of likelihood ratio criteria. Biometrika36, 317-346.
44. Broda, S. and Paolella, M.S. (2004) Saddlepoint approximations for the doubly noncentral tdistribution. Technical Report, Swiss Banking Institute, University of Zurich, Switzerland.
45. Bronson, D.A. (2001) Bootstrapping stochastic systems in survival analysis. Ph.D. dissertation, Department of Statistics, Colorado State University.
46. Buck, R.C. (1965)Advanced Calculus.New York: McGraw-Hill.
47. Butler, R.W. (1989) Approximate predictive pivots and densities. Biometrika76, 489-501.
48. Butler, R.W. (1997) System reliability, flowgraphs, and saddlepoint approximation. Technical Report, Department of Statistics, Colorado State University.
49. Butler, R.W. (1998) Generalized inverse Gaussian distributions and their Wishart connections.Scandinavian Journal of Statistics25, 69-75.
50. Butler, R.W. (2000) Reliabilities for feedback systems and their saddlepoint approximation. Statistical Science15, 279-298.
51. Butler, R.W. (2001) First passage distributions in semi-Markov processes and their saddlepoint approximation.Data Analysis from Statistical Foundations, ed E. Saleh. Huntington, NY: Nova Science Publishers.
52. Butler, R.W. (2003) Comments on “Ancillaries and Conditional Inference” by D.A.S. Fraser. Statistical Science19, 351-355.
53. Butler, R.W. (2007) Asymptotic hazard rates and uniformity of saddlepoint approximations. Technical Report, Department of Statistical Science, Southern Methodist University.
54. Butler, R.W. and Bronson, D.A. (2002) Bootstrapping survival times in stochastic systems by using saddlepoint approximations. Journal of the Royal Statistical Society series B64, 31-49.
55. Butler, R.W. and Huzurbazar, A.V. (1993) Prediction in stochastic networks. In Bulletin of the International Statistical Institute, Proceedings of the 49th Session, Firenze, Book 3, Topic 23.
56. Butler, R.W. and Huzurbazar, A.V. (1994) Bayesian prediction in stochastic systems. Technical Report, Department of Statistics, Colorado State University.
57. Butler, R.W. and Huzurbazar, A.V. (1997) Stochastic network models for survival analysis. Journal of the American Statistical Association92, 246-257.
58. Butler, R.W. and Huzurbazar, A.V. (2000) Bayesian prediction of waiting times in stochastic models. Canadian Journal of Statistics28, 311-325.
59. Butler, R.W., Huzurbazar, S., and Booth, J.G. (1992a) Saddlepoint approximation to generalized variance and Wilks’ statistic. Journal of the Royal Statistical Society series B79, 157-169.
60. Butler, R.W., Huzurbazar, S. and Booth, J.G. (1992b) Saddlepoint approximations for the Bartlett-Nanda-Pillai trace statistic in multivariate analysis. Biometrika79, 705-715.
61. Butler, R.W., Huzurbazar, S., and Booth, J.G. (1993) Saddlepoint approximations for tests of block independence, sphericity, and equal variances and covariances.Journal of the Royal Statistical Society series B55, 171-183.
62. Butler, R.W. and Paolella, M.S. (1998a) Saddlepoint approximations to the density and distribution of ratios of quadratic forms in normal variables with application to the sample autocorrelation function. Technical Report, Statistics Department, Colorado State University.
63. Butler, R.W. and Paolella, M.S. (1998b) Approximate distributions for the various serial correlograms. Bernoulli4, 497-518.
64. Butler, R.W. and Paolella, M.S. (2002) Calculating the density and distribution function for the singly and doubly noncentralF. Statistics and Computing12, 9-16.
65. Butler, R.W. and Paolella, M.S. (2004) Uniform saddlepoint approximations for ratios of quadratic forms. Technical Report, Colorado State University.
66. Butler, R.W. and Paige, R.L. (2007) Exact CDF computations for the largest eigenvalues of a matrix beta and Wishart. Technical Report, Department of Statistical Science, Southern Methodist University.
67. Butler, R.W. and Sutton, R.K. (1998) Saddlepoint approximation for multivariate CDF and probability computations in sampling theory and outlier testing. Journal of the American Statistical Association93, 596-604.
68. Butler, R.W., Sutton, R.K., Booth, J.G. and Ohman, P.A. (2005) Simulation-assisted saddlepoint approximation. Technical Report, Department of Statistics, Colorado State University.
69. Butler, R.W. and Wood, A.T.A. (2000) Laplace approximations for hypergeometric functions of matrix argument. Technical Report 00-05, Division of Statistics, University of Nottingham, available at:http://www.maths.nottingham.ac.uk/statsdiv/research/reports.html.
70. Butler, R.W. and Wood, A.T.A. (2002) Laplace approximation for hypergeometric functions of matrix argument. Annals of Statistics30, 1155-1177.
71. Butler, R.W. and Wood, A.T.A. (2003) Laplace approximations for Bessel functions of matrix argument. Journal of Computational and Applied Mathematics155, 359-382.
72. Butler, R.W. and Wood, A.T.A. (2004) A dimensional CLT for non-central Wilks’ lambda in multivariate analysis. Scandinavian Journal of Statistics31, 585-601.
73. Butler, R.W. and Wood, A.T.A. (2005) Approximation of power in multivariate analysis. Statistics and Computing15, 281-287.
74. Chapman, P.L., Butler, R.W., and Paige, R.L. (2007) Confidence bands for LD-100a in logistic regression by inverting sadddlepoint mid-p-values. Technical Report, Colorado State University.
75. Chernoff, H. (1954) On the distribution of the likelihood ratio. Annals of Mathematical Statistics25, 573-578.
76. Chow, S.C. and Shao, J. (1999) On the difference between the classical and inverse methods of calibration. Applied Statistics39, 219-228.
77. Chung, K.L. (2001)A Course in Probability Theory.New York: Academic Press.
78. Cochran, W. and Cox, G. (1957)Experimental Designs, Second edition. New York: Wiley.
79. Commenges, D. (1986) Semi-Markov and non-homogeneous Markov models in medicine. In Semi-Markov Models: Theory and Applications, ed. J. Janssen, pp. 423-436. New York: Plenum Press.
80. Cox, D.R. (1970)Analysis of Binary Data.London: Chapman and Hall.
81. Cox, D.R. and Hinkley, D.V. (1974)Theoretical Statistics.London: Chapman and Hall.
82. Cox, D.R. and Lewis, P.A.W. (1966)The Statistical Analysis of Series of Events.London: Methuen.
83. Cunningham, E.P. and Henderson, C.R. (1968) An iterative procedure for estimating fixed effects and variance components in mixed model situations. Biometrics24, 13-25.
84. Daniels, H.E. (1954) Saddlepoint approximations in statistics. Annals of Mathematical Statistics25, 631-650.
85. Daniels, H.E. (1956) The approximate distribution of serial correlation coefficients. Biometrika43, 169-185.
86. Daniels, H.E. (1958) Discussion of paper by D.R. Cox, Journal of the Royal Statistical Society series B20, 236-238.
87. Daniels, H.E. (1980) Exact saddlepoint approximations. Biometrika67, 59-63.
88. Daniels, H.E. (1983) Saddlepoint approximations for estimating equations. Biometrika70, 89-96.
89. Daniels, H.E. (1987) Tail probability approximations. International Statistical Review55, 37-48.
90. Daniels, H.E. (1992) A class of nearly exact saddlepoint approximations. In The Art of Statistical Science, ed. K.V. Mardia. New York: Wiley.
91. Daniels, H.E. and Young, G.A. (1991) Saddlepoint approximation for the Studentized mean, with an application to the bootstrap. Biometrika78, 169-179.
92. Davison, A.C. (1986) Approximate predictive likelihood. Biometrika73, 323-332.
93. Davison, A.C. (1988) Approximate conditional inference in generalized linear models. Journal of the Royal Statistical Society series B50, 445-451.
94. Davison, A.C. and Hinkley, D.V. (1988) Saddlepoint approximations in resampling methods. Biometrika75, 417-431.
95. Davison, A.C. and Hinkley, D.V. (1997)Bootstrap Methods and their Application.Cambridge: Cambridge University Press.
96. Davison, A.C. and Wang, S. (2002) Saddlepoint approximations as smoothers. Biometrika89, 933-938.
97. DiCiccio, T.J., Field, C.A., and Fraser, D.A.S. (1990) Approximations for marginal tail probabilities and inference for scalar parameters. Biometrika77, 77-95.
98. DiCiccio, T.J. and Martin, M.A. (1991) Approximations of marginal tail probabilities for a class of smooth functions with applications to Bayesian and conditional inference. Biometrika78, 891-902.
99. DiCiccio, T.J., Martin, M.A., and Young, G.A. (1992a) Analytic approximations for iterated bootstrap confidence intervals. Statistics and Computing2, 161-171.
100. DiCiccio, T.J., Martin, M.A., and Young, G.A. (1992b) Fast and accurate approximate double bootstrap confidence intervals. Biometrika79, 285-295.
101. DiCiccio, T.J., Martin, M.A., and Young, G.A. (1993) Analytical approximations to conditional distribution functions. Biometrika80, 285-295.
102. DiCiccio, T.J., Martin, M.A., and Young, G.A. (1994) Analytic approximations to bootstrap distribution functions using saddlepoint approximations. Statistica Sinica4, 281-295.
103. Downton, F. (1970) Bivariate exponential distributions in reliability theory. Journal of the Royal Statistical Society series B32, 408-417.
104. Durbin, J. (1980a) Approximations for densities of sufficient statistics. Biometrika67, 311-333.
105. Durbin, J. (1980b) The approximate distribution of serial correlation coefficients calculated from residuals on Fourier series. Biometrika67, 335-350.
106. Durbin, J. and Watson, G.S. (1950) Testing for serial correlation in least squares regression I. Biometrika37, 409-428.
107. Durbin, J. and Watson, G.S. (1951) Testing for serial correlation in least squares regression II. Biometrika38, 159-178.
108. Eaton, M.L. (1983)Multivariate Statistics.Third edition. New York: McGraw-Hill.
109. Efron, B. (1975) Defining the curvature of a statistical problem (with applications to second-order efficiency) (with discussion). Annals of Statistics3, 1189-1242.
110. Efron, B. and Hinkley, D.V. (1978) Assessing the accuracy of the maximum likelihood estimator: Observed versus expected information (with discussion). Biometrika65, 457-487.
111. Esscher, F. (1932) On the probability function in the collective theory of risk. Skand. Akt. Tidsskr.15, 78-86.
112. Fahrmeir, L. and Tutz, G. (1994)Multivariate Statistical Modeling Based on Generalized Linear Models.New York: Springer-Verlag.
113. Feller, W. (1968)An Introduction to Probability Theory and its Applications, vol. I, Third edition. New York: Wiley.
114. Feller, W. (1971)An Introduction to Probability Theory and its Applications, vol. II, Second edition. New York: Wiley.
115. Feuerverger, A. (1989) On the empirical saddlepoint approximation, Biometrika76, 457-464.
116. Field, C. (1982) Small sample asymptotic expansions for the multivariate M-estimates. Annals of Statistics10, 672-689.
117. Field, C.A. and Hampel, F.R. (1982) Small-sample asymptotic distributions of M-estimates of location. Biometrika69, 29-46.
118. Field, C.A. and Ronchetti, E. (1990)Small Sample Asymptotics.Institute of Mathematical Statistics Lecture Notes 13, Hayward, CA: Institute of Mathematical Statistics.
119. Fieller, E.C. (1954) Some problems on interval estimation. Journal of the Royal Statistical Society series B16, 175-185.
120. Fisher, R.A. (1934) Two new properties of mathematical likelihood. Proceedings of the Royal Society A144, 285-307.
121. Fisher, R.A. (1961) Sampling the reference set. Sankhya23, 3-8.
122. Fisher, R.A. (1973)Statistical Methods and Scientific Inference,3rd ed., Edinburgh: Oliver & Boyd.
123. Fisher, R.A. (1990)Statistical Methods, Experimental Design, and Scientific Inference.Oxford: Oxford University Press.
124. Fisher, R.A. and Healy, M.J.R. (1958) New tables of Behrens’ test of significance. Journal of the Royal Statistical Society series B18, 212-216.
125. Fokianos, K. (2001) Truncated Poisson regression for time series of counts. Scandinavian Journal of Statistics28, 645-659.
126. Fraser, D.A.S. (1968)The Structure of Inference.Huntington, NY: Krieger.
127. Fraser, D.A.S. (1979)Inference and Linear Models.New York: McGraw-Hill.
128. Fraser, D.A.S. (1990) Tail probabilities from observe likelihoods. Biometrika77, 65-76.
129. Fraser, D.A.S. (2003) Likelihood for component parameters. Biometrika90, 327-339.
130. Fraser, D.A.S. (2004) Ancillaries and conditional inference. Statistical Science19, 333-369.
131. Fraser, D.A.S. and Reid, N. (1993) Third order asymptotic models: likelihood functions leading to accurate approximations for distribution functions. Statistica Sinica3, 67-82.
132. Fraser, D.A.S. and Reid, N. (1995) Ancillaries and third order inference. Utilitas Mathematica47, 33-53.
133. Fraser, D.A.S. and Reid, N. (2001) Ancillary information for statistical inference. Empirical Bayes and Likelihood Inference. Lecture Notes in Statistics148, 185-209. New York: Springer.
134. Fraser, D.A.S., Reid, N., and Wong, A. (1991) Exponential linear models: a two-pass procedure for saddlepoint approximation. Journal of the Royal Statistical Society series B53, 483-492.
135. Fraser, D.A.S., Reid, N., and Wu, J. (1999a) A simple general formula for tail probabilities for frequentist and Bayesian inference. Biometrika86, 249-264.
136. Fraser, D.A.S., Wong, A., and Wu, J. (1999b) Regression analysis, nonlinear or nonnormal: simple and accurate pvalues from likelihood analysis. Journal of the American Statistical Association94, 1286-1295.
137. Gatto, R. and Jammalamadaka, S.R. (1999) A conditional saddlepoint approximation for testing problems. Journal of the American Statistical Association94, 533-541.
138. Geary, R.C. (1944) Extension of a theorem by Harald Cramer on the frequency distribution of the quotient of two variables. Journal of the Royal Statistical Society series B17, 56-57.
139. Glaser, R.E. (1976) Exact critical values of Bartlett's test for homogeneity of variances. Journal of the American Statistical Association71, 488-490.
140. Gross, A.J., Clark, V.A., and Liu, V. (1970) Estimation of survival parameters where one or two organs must function for survival. Biometrics27, 369-377.
141. Gross, A.J., Clark, V.A., and Liu, V. (1971) Estimation of survival parameters where one or two organs must function for survival. Biometrics27, 369-377.
142. Gupta, A.K. and Tang, J. (1984) Distribution of likelihood ratio statistic for testing equality of covariance matrices of multivariate Gaussian models. Biometrika71, 555-559.
143. Gupta, R.D. and Richards, D.S.P. (1985) Hypergeometric functions of scalar matrix argument are expressible in terms of classical hypergeometric functions. SIAM Journal on Mathematical Analysis16, 852-858.
144. Haight, F.A. and Breuer, M.A. (1960) The Borel-Tanner distribution. Biometrika47, 143-150.
145. Hampel, F.R. (1973) Small sample asymptotics. In Proceedings of the Prague Symposium on Asymptotic Statistics, ed. J. Hajek. Prague: Charles University.
146. Hannig, J., Wang, C.M., and Iyer, H.K. (2003) Uncertainty calculation for the ratio of dependent measurements. Metrologia40, 177-183.
147. Henrici, P. (1977)Applied and Computational Complex Analysis, vol. II: Special Functions-Integral Transforms-Asymptotics-Continued Fractions.New York: Wiley.
148. Henshaw, R.C. (1966) Testing single equation least squares regression models for autocorrelated disturbances. Econometrica34, 646-660.
149. Hill, B.M. (1968) Posterior distribution of percentiles: Bayes’ theorem for sampling from a population. Journal of the American Statistical Association63, 677-691.
150. Hinkley, D.V. (1980a) Likelihood. Canadian Journal of Statistics2, 151-163.
151. Hinkley D.V. (1980b) Likelihood as an approximate pivotal distribution. Biometrika 67, 287-292.
152. Hinkley, D.V. and Shi, S. (1989) Importance sampling and the nested bootstrap. Biometrika76, 435-446.
153. Hinkley, D.V. and Wei, B.C. (1984) Improvement of jackknife confidence limit methods. Biometrika71,331-339.
154. Holgate, P. (1964) Estimation for the bivariate Poisson distribution. Biometrika51, 241-245.
155. Hougaard, P. (1988) Comment on Reid (1988). Statistical Science3, 230-231.
156. Hpyland, A. and Rausand, M. (1994)System Reliability Theory, Models and Statistical Methods.New York: Wiley.
157. Imhof, P. (1961) Computing the distribution of quadratic forms in normal variables. Biometrika48, 419-426.
158. Jeffreys, H. (1961)Theory of Probability. Oxford: Oxford University Press.
159. Jensen, J.L. (1988) Uniform saddlepoint approximations. Advances in Applied Probability20, 622-634.
160. Jensen, J.L. (1991a) Uniform saddlepoint approximations and log-concave densities. Journal of the Royal Statistical Society series B53, 157-172.
161. Jensen, J.L. (1991b) A large deviation type approximation for the ‘Box class’ of likelihood ratio criteria. Journal of the American Statistical Association,86, 437-440.
162. Jensen, J.L. (1992) The modified signed log likelihood statistic and saddlepoint approximations. Biometrika79, 693-703.
163. Jensen, J.L. (1995)Saddlepoint Approximations.Oxford: Clarendon Press.
164. Jing, B. and Robinson, J. (1994) Saddlepoint approximations for marginal and conditional probabilities of transformed variables. Annals of Statistics22, 1115-1132.
165. Jing, B., Feuerverger, A., and Robinson, J. (1994) On the bootstrap saddlepoint approximations. Biometrika81, 211-215.
166. Johnson, N.L. and Kotz, S. (1969)Distributions in Statistics: Discrete Distributions.New York: Wiley.
167. Johnson, N.L. and Kotz, S. (1970)Distributions in Statistics: Continuous Univariate Distributions-2. New York: Wiley.
168. Johnson, N.L. and Kotz, S. (1972)Continuous Multivariate Distributions.New York: Wiley.
169. Johnson, N.L. and Kotz, S. (1986) Encyclopedia ofStatistical Sciences.New York: Wiley.
170. Johnson, N.L., Kotz, S., and Balakrishnan, N. (1995)Continuous Univariate Distributions, vol. II. Second edition. New York: Wiley.
171. Johnson, N.L., Kotz, S. and Kemp, A.W. (1992)Univariate Discrete Distributions.Second edition. New York: Wiley.
172. Johnson, R. and Johnson, N. (1980)Survival Models and Data Analysis.New York: Wiley
173. Jprgensen, B. (1997) The Theory of Dispersion Models.London: Chapman and Hall.
174. Kalbfleisch, J.D. and Sprott, D.A. (1970) Application of likelihood methods to models involving large numbers of parameters (with Discussion). Journal of the Royal Statistical Society series B32, 175-208.
175. Kalbfleisch, J.D. and Sprott, D.A. (1973) Marginal and conditional likelihoods. SankhyaA35, 311-328.
176. Karlin, S. and Taylor, H. (1981)A Second Course in Stochastic Processes.New York: Academic Press.
177. Kay, S.M., Nuttall, A.H., and Baggenstoss, P.M. (2001) Multidimensional probability density function approximations for detection, classification, and model order selection. IEEE Transactions on Signal Processing49, 2240-2252.
178. Kendall, M.G. and Stuart, A. (1969)The Advanced Theory of Statistics, vol. I. Third edition. New York: Hafner.
179. Kendall, M.G. and Stuart, A. (1973)The Advanced Theory of Statistics, vol. II, Third edition. New York: Hafner.
180. Kibble, W.F. (1941) A two-variate gamma type distribution. Sankhya5, 137-150.
181. Kim, D. and Agresti, A. (1995) Improved exact inference about conditional association in three-way contingency tables. Journal of the American Statistical Association90, 632-639.
182. Kolassa, J.E. (1994)Series Approximation Methods in Statistics.New York: Springer-Verlag.
183. Kolassa, J.E. (1996) Higher-order approximations to conditional distribution functions. Annals of Statistics,24, 353-364.
184. Kolassa, J.E. (2003) Multivariate saddlepoint tail probability approximations. Annals of Statistics,31, 274-286.
185. Kolassa, J.E. (2004) Approximate multivariate conditional inference using the adjusted profile likelihood. Canadian Journal of Statistics32, 5-14.
186. Kolassa, J.E. and Robinson, J. (2006) Conditional saddlepoint approximations for non-continuous and non-lattice distributions. Journal of Statistical Planning and Inference.To appear.
187. Kres, H. (1983)Statistical Tables for Multivariate Analysis.New York: Springer-Verlag.
188. Krishnan, M. (1967) The moments of a doubly noncentral t-distribution. Journal of the American Statistical Association62, 278-287.
189. Kulp, R.W. and Nagarsenkar, B.N. (1984) An asymptotic expansion of the nonnull distribution of Wilks criterion for testing the multivariate linear hypothesis. Annals of Statistics12, 1576-1583.
190. Lagakos, S. (1976) A stochastic model for censored survival time in the presence of an auxiliary variable. Biometrics32, 551-559.
191. Lawless, J.F. (1973) Conditional versus unconditional confidence intervals for the parameters of the Weibull distribution. Journal of the American Statistical Association68, 665-669.
192. Lawless, J.F. (1974) Approximations to confidence intervals for parameters in the extreme value and Weibull distributions. Biometrika61, 123-129.
193. Lee, Y.-S. (1971) Distribution of the canonical correlations and asymptotic expansions for distributions of certain independence test statistics. Annals of Mathematical Statistics42, 526-537.
194. Lehmann, E.L. (1986)Testing Statistical Hypotheses, Second edition. New York: Wiley.
195. Lehmann, E.L. and D’Abrera, H.J.M. (1975)Nonparametrics: Statistical Methods Based on Ranks. San Francisco: Holden Day.
196. Lieberman, O. (1994a) Saddlepoint approximation for the least squares estimator in first-order autoregression. Biometrika81, 807-11. Corrigendum 1996 83, 246.
197. Lieberman, O. (1994b) Saddlepoint approximation for the distribution of a ratio of quadratic forms in normal variables. Journal of the American Statistical Association89, 924-928.
198. Lieblein, J. and Zelen, M. (1956) Statistical investigation of the fatigue life of deep groove ball bearings. Journal of Research, National Bureau of Standards57, 273-316.
199. Lloyd, D.K. and Lipow, M. (1962)Reliability: Management, Methods, and Mathematics.Englewood Cliffs: Prentice Hall.
200. Lugannani, R. and Rice, S.O. (1980) Saddlepoint approximations for the distribution of the sum of independent random variables. Advances in Applied Probability12, 475-490.
201. Lyons, B. and Peters, D. (2000). Applying Skovgaard's modified directed likelihood statistic to mixed linear models. Journal of Statistical Computation and Simulation65, 225-242.
202. Magnus, J.R. and Neudecker, H. (1988)Matrix Differential Calculus with Applications in Statistics and Econometrics.New York: Wiley.
203. Marsh, P.W.R. (1998) Saddlepoint approximations and non-central quadratic forms.Econometric Theory14, 539-559.
204. Martz, R.A. and Waller, H.F. (1982)Bayesian Reliability Analysis.New York: Wiley.
205. Mathai, A.M. and Katiyar, R.S. (1979) Exact percentage points for testing independence. Biometrika66, 353-356.
206. McCullagh, P. (1987)Tensor Methods in Statistics.New York: Chapman and Hall.
207. McCullagh, P. and Nelder, J.A. (1989)Generalized Linear Models2nd ed. London: Chapman and Hall.
208. McGregor, J.R. (1960) An approximate test for serial correlation in polynomial regression. Biometrika47, 111-119.
209. Medhi, J. (1994)Stochastic Processes, Second edition. New York: Wiley.
210. Mendoza, J.L. (1980) A significance test for multisample sphericity. Psychometrika45, 495-498.
211. Milliken, G.A. and Johnson, D.E. (1984)Analysis of Messy Data.Belmont, CA: Wadsworth, Inc.
212. Monti, A.C. and Ronchetti, E. (1993) On the relationship between empirical likelihood and empirical saddlepoint approximation for multivariate M-estimators. Biometrika80, 329-338.
213. Morgan, B.J.T. (1992)Analysis ofQuantal Response Data.London: Chapman and Hall.
214. Morrison, D.F. (1976). Multivariate statistical methods,2nd ed. New York: McGraw-Hill.
215. Morrison, D.F. (1990)Multivariate Statistical Methods,3rd ed. New York: McGraw-Hill.
216. Mudholkar, G.S., Trivedi, M.C., and Lin, C.T. (1982) On approximation to the distribution of the likelihood ratio statistic for testing complete independence. Technometrics24, 139-143.
217. Muirhead, R.J. (1972). On the test of independence between two sets of variates. Annals of Mathematical Statistics43, 1491-1497.
218. Muirhead, R.J. (1982)Aspects of Multivariate Statistical Theory.New York: Wiley.
219. Muller, K.E., LaVange, L.M., Ramey, S.L., and Ramey, C.T. (1992) Power calculations for general linear multivariate models including repeated measures applications. Journal of the American Statistical Association87, 1209-1226.
220. Muller, K.E. and Peterson, B.L. (1984) Practical methods for computing power in testing the multivariate general linear hypothesis. Computational Statistics and Data Analysis2, 143-158.
221. Nagarsenkar, B.N. (1975) Percentage points of Wilks’ Avc criterion. Communications in Statistics4, 629-641.
222. Nagarsenkar, B.N. and Pillai, K.C.S. (1973) The distribution of the sphericity test criterion. Journal of Multivariate Analysis3, 226-235.
223. Neuts, M.F. (1981)Matrix-geometric Solutions in Stochastic Models.Baltimore, MD: Johns Hopkins University Press.
224. Neyman, J. and Scott, E.L. (1948) Consistent estimates based on partially consistent observations. Econometrica16, 1-32.
225. Norris, J.R. (1997)Markov Chains.Cambridge: Cambridge University Press.
226. Pace, L. and Salvan, A. (1997)Principles of Statistical Inference from a Neo-Fisherian Perspective. Singapore: World Scientific Publishing.
227. Paolella, M.S. (1993)Saddlepoint applications in regressions models.M.S. Thesis, Department of Statistics, Colorado State University.
228. Paolella, M.S. and Butler, R.W. (1999) Approximating the density, distribution, and moments of ratios of quadratic forms in normal variables with application to the sample autocorrelation function. Technical Report, Department of Statistics, Colorado State University.
229. Patterson, H.D. and Thompson, R. (1971) Recovery of interblock information when block sizes are unequal. Biometrika58, 545-554.
230. Pedersen, B.V. (1981) A comparison of the Efron-Hinkley ancillary and the likelihood ratio ancillary in a particular example. Annals of Statistics9, 1328-1333.
231. Phillips, P.C.B. (1978) Edgeworth and saddlepoint approximations in the first-order non-circular autoregression. Biometrika65, 91-98.
232. Phillips, P.C.B. (1982) The true characteristic function of the Fdistribution. Biometrika69,261-264.
233. Phillips, P.C.B. (1985) The distribution of matrix quotients. Journal of Multivariate Analysis16, 157-161.
234. Pierce, D.A. and Peters, D. (1992) Practical use of higher order asymptotics for multiparameter exponential families (with Discussion). Journal of the Royal Statistical Society series B54, 701-737.
235. Pillai, K.C.S. (1985) “Multivariate analysis of variance” entry in the Encyclopedia of Statistical Scienceed. N.L. Johnson and S. Kotz. New York: Wiley.
236. Pillai, K.C.S. and Mijares, T.A. (1959) On the moments of the trace of a matrix and approximations to its distribution. Annals of Mathematical Statistics30, 1135-1140.
237. Polansky, A.M. (1999) Upper bounds on the true coverage of bootstrap percentile type confidence intervals. American Statistician53, 362-369.
238. Priestley, M.B. (1981)Spectral Analysis and Time Series.New York: Academic Press.
239. Press, S.J. (1972)Applied Multivariate Analysis.New York: Holt, Rinehart and Winston.
240. Quine, M.P. (1994) Probability approximations for divisible discrete distributions. Australian Journal of Statistics36, 339-349.
241. Reid, N. (1988) Saddlepoint methods and statistical inference. Statistical Science3, 213-238.
242. Reid, N. (1995) The roles of conditioning in inference. Statistical Science10, 138-157.
243. Reid, N. (1996) Likelihood and higher-order approximations to tail areas: A review and annotated bibliography. Canadian Journal of Statistics24, 141-166.
244. Reid, N. (2003) Asymptotics and the theory of inference. Annals of Statistics31, 1695-1731.
245. Rice, J.A. (1995)Mathematical Statistics and Data Analysis.Second edition. Belmont, CA: Wadsworth, Inc.
246. Robinson, J. (1982) Saddlepoint approximations for permutation tests and confidence intervals. Journal of the Royal Statistical Society series B44, 91-101.
247. Robinson, J., Hoglund, T., Holst, L., and Quine, M.P. (1990) On approximating probabilities for small and large deviations in Rd. Annals of Probability18, 727-753.
248. Rockafellar, R.T. (1970)Convex Analysis, Princeton, NJ: Princeton University Press.
249. Ronchetti, E. and Welsh, A.H. (1994) Empirical saddlepoint approximations for multivariate M-estimators. Journal of the Royal Statistical Society series B56, 313-326.
250. Ross, S.L. (1974)Differential Equations.Second edition. Lexington, MA: Xerox College Publishing.
251. Ross, S.M. (1983)Stochastic Processes.New York: Wiley.
252. Routledge, R.D. (1994) Practicing safe statistics with the mid-p. Canadian Journal of Statistics22, 103-110.
253. Rubin, D.B. (1981) The Bayesian bootstrap. Annals of Statistics9, 130-134.
254. Sartori, N. (2003) Modified profile likelihoods in models with stratum nuisance parameters. Biometrika90, 533-549.
255. Sartori, N., Bellio, R., Pace, L., and Salvan, A. (1999) The directed modified profile likelihood in models with many nuisance parameters. Biometrika86, 735-742.
256. Scheffe, H. (1959)The Analysis of Variance.New York: Wiley.
257. Seneta, E. (1981)Non-negative Matrices and Markov Chains.New York: Springer-Verlag.
258. Severini, T.A. (2000a)Likelihood Methods in Statistics.Oxford: Oxford University Press.
259. Severini, T.A. (2000b) The likelihood ratio approximation to the conditional distribution of the maximum likelihood estimator in the discrete case. Biometrika87, 939-945.
260. Shun Z. and McCullagh, P. (1995) Laplace approximation of high dimensional integrals. Journal of the Royal Statistical Society series B57, 749-760.
261. Skovgaard, I.M. (1985) Large deviation approximations for maximum likelihood estimators. Probability and Mathematical Statistics6, 89-107.
262. Skovgaard, I.M. (1987) Saddlepoint expansions for conditional distributions. Journal of Applied Probability24, 875-887.
263. Skovgaard, I.M. (1990) On the density of minimum contrast estimators. Annals of Statistics18, 779-789.
264. Skovgaard, I.M. (1996) An explicit large-deviation approximation to one parameter tests. Bernoulli2, 145-165.
265. Skovgaard, I.M. (2001) Likelihood asymptotics. Scandinavian Journal of Statistics28, 3-32.
266. Solberg, J.J. (1975) A graph theoretic formula for the steady state distribution of finite Markov processes. Management Science21, 1040-1048.
267. Spady, R.H. (1991) Saddlepoint approximations for regression models. Biometrika78, 879-889.
268. Srivastava, M.S. and Khatri, C.G. (1979)An Introduction to Multivariate Statistics.New York: North-Holland.
269. Srivastava, M.S. and Yau, W.K. (1989) Saddlepoint method for obtaining tail probability of Wilks’ likelihood ratio test. Journal of Multivariate Analysis31, 117-126.
270. Strawderman, R.L., Casella, G., and Wells, M.T. (1996) Practical small-sample asymptotics for regression problems. Journal of the American Statistical Association91, 643-654. Corrigendum 1997 92, 1657.
271. Strawderman, R.L. and Wells, M.T. (1998) Approximately exact inference for common odds ratio in several 2 x 2 tables. Journal of the American Statistical Association93, 1294-1307.
272. Sugiura, N. (1973a) Further asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis. Annals of the Institute of Statistical Mathematics25, 153-163.
273. Sugiura, N. (1973b) Asymptotic non-null distributions of the likelihood ratio criteria for covariance matrix under local alternatives. Annals of Statistics1, 718-728.
274. Sugiura, N. (1974) Asymptotic formulas for the hypergeometric function 2F1 of matrix argument, useful in multivariate analysis. Annals of the Institute of Statistical Mathematics26, 117-125.
275. Sugiura, N. and Fujikoshi, Y. (1969) Asymptotic expansion of the non-null distributions of the likelihood ratio criteria for multivariate linear hypothesis and independence. Annals ofMathematical Statistics40, 942-952.
276. Sugiyama, T. (1967). Distribution of the largest latent root and the smallest latent root of the generalized Bstatistic and Fstatistic in multivariate analysis. Annals of Mathematical Statistics38, 1152-1159.
277. Taylor, H.M. and Karlin, S. (1998)An Introduction to Stochastic Modeling.Third edition. New York: Academic Press.
278. Temme, N.M. (1982) The uniform asymptotic expansion of a class of integrals related to cumulative distribution functions. SIAM Journal on Mathematical Analysis13, 239-253.
279. Thoman, D.R., Bain, L.J., and Antle, C.E. (1969) Inferences for the parameters of the Weibull distribution. Technometrics11, 445-460.
280. Tierney, L. and Kadane, J.B. (1986) Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association81, 82-86.
281. Tiku, M.L. (1972) A note on the distribution of the doubly noncentral Fdistribution. Australian Journal of Statistics14, 37-40.
282. Tiku, M.L. and Yip, D.Y.N. (1978) A four moment approximation based on the Fdistribution. Australian Journal of Statistics20, 257-261.
283. Tingley, M. and Field, C. (1990) Small-sample confidence intervals. Journal of the American Statistical Association85, 427-434.
284. Vinod, H.D. (1973) Generalization of the Durbin-Watson statistic for higher order autoregressive processes. Communications in Statistics A2, 115-144.
285. Wang, S. (1990) Saddlepoint approximations or bivariate distributions. Journal of Applied Probability27, 586-597.
286. Wang, S. (1992) Tail probability approximations in the first-order non-circular autoregression. Biometrika79, 431-434.
287. Wang, S. and Carroll, R.J. (1999) High-order accurate methods for retrospective sampling problems. Biometrika86, 881-897.
288. Wicksell, S.D. (1933) On correlation surfaces of type III. Biometrika25, 121-136.
289. Wilks, S.S. (1946) Sample criteria for testing equality of means, equality of variances, and equality of covariances in a normal multivariate distribution. Annals of Mathematical Statistics17,257-281
290. Wood, A.T.A., Booth, J.G., and Butler, R.W. (1992) Saddlepoint approximations to the CDF for some statistics with non-normal limit distributions. Technical report, Colorado State University.
291. Wood, A.T.A., Booth, J.G., and Butler, R.W. (1993) Saddlepoint approximations to the CDF for some statistics with non-normal limit distributions. Journal of the American Statistical Association88, 680-686.
292. Zeger, S.L. (1988) A regression model for time series of counts. Biometrika75, 621-629.