Introduction to stein's method, an

Introduction to Stein's Method, an

Volumn , Issue , 2005, Pages 1-225

  Barbour, A D ^a   Chen, Louis H Y ^b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85114980833     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/5792     Document Type: Book

References (185)

1. P. Baldi & Y. Rinott (1989) On normal approximation of distributions in terms of dependency graph. Ann. Probab. 17, 1646-1650.
2. P. Baldi, Y. Rinott & C. Stein (1989) A normal approximation for the number of local maxima of a random function on a graph. In: Probability, statistics, and mathematics. Papers in honor of Samuel Karlin, Eds: T. W. Anderson, K. B. Athreya, D. L. Iglehart, pp. 59-81. Academic Press, Boston.
3. A. D. Barbour & L. H. Y. Chen (1992) On the binary expansion of a random integer. Statist. Probab. Lett. 14, 235-241.
4. A. D. Barbour & P. Hall (1984) Stein’s method and the Berry-Esseen theorem. Austral. J. Statist. 26, 8-15.
5. P. van Beeck (1972) An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality. Z. Wahrsch. verw. Geb. 23, 187-196.
6. A. Bikelis (1966) Estimates of the remainder in the central limit theorem. Litovsk. Mat. Sb. 6, 323-346 (in Russian).
7. E. Bolthausen (1984) An estimate of the remainder in a combinatorial central limit theorem. Z. Wahrsch. verw. Geb. 66, 379-386.
8. E. Bolthausen & F. Gotze (1993) The rate of convergence for multivariate sampling statistics. Ann. Statist. 21, 1692-1710.
9. L. H. Y. Chen (1986) The rate of convergence in a central limit theorem for dependent random variables with arbitrary index set. IMA Preprint Series #243, Univ. Minnesota.
10. L. H. Y. Chen (1998) Stein’s method: some perspectives with applications. In: Probability towards 2000, Eds: L. Accardi & C. C. Heyde, Lecture Notes in Statistics128, pp. 97-122. Springer-Verlag, Berlin.
11. L. H. Y. Chen (2000) Non-uniform bounds in probability approximations using Stein’s method. In: Probability and statistical models with applications: a volume in honor of Theophilos Cacoullos, Eds: N. Balakrishnan, Ch. A. Charalambides & M. V. Koutras, pp. 3-14. Chapman & Hall/CRC Press, Boca Raton, Florida.
12. L. H. Y. Chen & Q. M. Shao (2001) A non-uniform Berry-Esseen bound via Stein’s method. Probab. Theory Rel. Fields 120, 236-254.
13. L. H. Y. Chen & Q. M. Shao (2004a) Normal approximation under local dependence. Ann. Probab. 32, 1985-2028.
14. L. H. Y. Chen & Q. M. Shao (2004b) Normal approximation for non-linear statistics using a concentration inequality approach. Preprint.
15. A. Dembo & Y. Rinott (1996) Some examples of normal approximations by Stein’s method. In: Random Discrete Structures, Eds: D. Aldous & R. Pe-mantle, pp. 25-44. Springer, New York.
16. P. Diaconis (1977) The distribution of leading digits and uniform distribution mod 1. Ann. Probab. 5, 72-81.
17. P. Diaconis & S. Holmes (2004) Stein’s method: expository lectures and applications. IMS Lecture Notes, Vol. 46, Hayward, CA.
18. P. Diaconis, S. Holmes & G. Reinert (2004) Use of exchangeable pairs in the analysis of simulations. In: Stein’s method: expository lectures and applications, Eds: P. Diaconis & S. Holmes, pp. 1-26. IMS Lecture Notes Vol. 46, Hayward, CA.
19. 1 bounds for asymptotic normality of m-dependent sums using Stein’s technique. Ann. Probab. 2, 522-529.
20. C. G. Esseen (1945) Fourier analysis of distribution functions: a mathematical study of the Laplace-Gaussian law. Acta Math. 77, 1-125.
21. W. Feller (1968) On the Berry-Esseen theorem. Z. Wahrsch. verw. Geb. 10, 261-268.
22. L. Goldstein (2005) Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing. J. Appl. Probab. 42 (to appear).
23. L. Goldstein & G. Reinert (1997) Stein’s method and the zero bias transformation with application to simple random sampling. Ann. Appl. Probab. 7, 935-952.
24. L. Goldstein & Y. Rinott (1996) Multivariate normal approximations by Stein’s method and size bias couplings. Adv. Appl. Prob. 33, 1-17.
25. F. Götze (1991) On the rate of convergence in the multivariate CLT. Ann. Probab. 19, 724-739.
26. p bound for the remainder in a combinatorial central limit theorem. Ann. Probab. 6, 231-249.
27. S. V. Nagaev (1965) Some limit theorems for large deviations. Theory Probab. Appl. 10, 214-235.
28. L. Paditz (1989) On the analytical structure of the constant in the nonuniform version of the Esseen inequality. Statistics 20, 453-464.
29. V. V. Petrov (1995) Limit theorems of probability theory: sequences of independent random variables. Oxford Studies in Probability 4, Clarendon Press, Oxford.
30. Y. Rinott (1994) On normal approximation rates for certain sums of dependent random variables. J. Comput. Appl. Math. 55, 135-143.
31. Y. Rinott & V. Rotar (1996) A multivariate CLT for local dependence with n-1/2 logro rate and applications to multivate graph related statistics. J. Multiv. Anal. 56, 333-350.
32. Y. Rinott & V. Rotar (2000) Normal approximations by Stein’s method. Decis. Econ. Finance 23, 15-29.
33. p (p > 2) spanned by sequences of independent random variables. Israel J. Math. 8, 273-303.
34. C. Stein (1972) A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proc. Sixth Berkeley Symp. Math. Statist. Prob. 2, 583-602. Univ. California Press, Berkeley, CA.
35. C. STEIN (1986) Approximation computation of expectations. IMS Lecture Notes Vol. 7, Hayward, CA.
36. D. W. Stroock (1993) Probability theory: an analytic view. Cambridge Univ. Press, Cambridge, U.K.
37. D. J. Aldous (1989) Probability approximations via the Poisson clumping heuristic. Springer, New York.
38. R. Arratia, L. Goldstein & L. Gordon (1989) Two moments suffice for Poisson approximations: the Chen-Stein method. Ann. Probab. 17, 9-25.
39. R. Arratia, L. Goldstein & L. Gordon (1990) Poisson approximation and the Chen-Stein method. Statist. Set. 5, 403-434.
40. A. D. Barbour (1987) Asymptotic expansions in the Poisson limit theorem. Ann. Probab. 15, 748-766.
41. A. D. Barbour (1988) Stein’s method and Poisson process convergence. J. Appl. Probab. 15A, 175-184.
42. A. D. Barbour (1997) Stein’s method. In: Encyclopedia of statistical science, 2nd ed. Wiley, New York.
43. A. D. Barbour & T. C. Brown (1992a) Stein’s method and point process approximation. Stoch. Proc. Appl. 43, 9-31.
44. A. D. Barbour & T. C. Brown (1992b) The Stein-Chen method, point processes and compensators. Ann. Probab. 20, 1504-1527.
45. A. D. Barbour & V. Cekanavicius (2002) Total variation asymptotics for sums of independent integer random variables. Ann. Probab. 30, 509-545.
46. A. D. Barbour, L. H. Y. Chen & K. P. Choi (1995) Poisson approximation for unbounded functions, I: independent summands. Statist. Sinica 5, 749-766.
47. A. D. Barbour, L. H. Y. Chen & W.-L. Loh (1992) Compound Poisson approximation for nonnegative random variables via Stein’s method. Ann. Probab. 20, 1843-1866.
48. A. D. Barbour & O. Chryssaphinou (2001) Compound Poisson approximation: a user’s guide. Ann. Appl. Probab. 11, 964-1002.
49. A. D. Barbour & G. K. Eagleson (1983) Poisson approximation for some statistics based on exchangeable trials. Adv. Appl. Probab. 15, 585-600.
50. A. D. Barbour & P. Hall (1984) On the rate of Poisson convergence. Math. Proc. Cambridge Philos. Soc. 95, 473-480.
51. A. D. Barbour & L. Holst (1989) Some applications of the Stein-Chen method for proving Poisson convergence. Adv. Appl. Probab. 21, 74-90.
52. A. D. Barbour, L. Holst & S. Janson (1992) Poisson approximation. Oxford University Press.
53. A. D. Barbour & J. L. Jensen (1989) Local and tail approximations near the Poisson limit. Scand. J. Statist. 16, 75-87.
54. A. D. Barbour & M. Mansson (2000) Compound Poisson approximation and the clustering of random points. Adv. in Appl. Probab. 32, 19-38.
55. A. D. Barbour & M. Mansson (2002) Compound Poisson process approximation. Ann. Probab. 30, 1492-1537.
56. A. D. Barbour & S. Utev (1998) Solving the Stein equation in compound Poisson approximation. Adv. Appl. Probab. 30, 449-475.
57. A. D. Barbour & S. Utev (1999) Compound Poisson approximation in total variation. Stock. Proc. Appl. 82, 89-125.
58. A. D. Barbour & A. Xia (1999) Poisson perturbations. ESAIM Probab. Statist. 3, 131-150.
59. A. D. Barbour & A. xla (2000) Estimating Stein’s constants for compound Poisson approximation. Bernoulli 6, 581-590.
60. I. S. Borisov (2002) Poisson approximation for expectations of unbounded functions of independent random variables. Ann. Probab. 30, 1657-1680.
61. L. Le Cam (1960) An approximation theorem for the Poisson binomial distribution. Pacific J. Math. 10, 1181-1197.
62. L. Le Cam (1965) On the distribution of sums of independent random variables. In: J. Neyman & L. Le Cam (eds). Bernoulli, Bayes, Laplace. Springer, New York.
63. L. H. Y. Chen (1975) Poisson approximation for dependent trials. Ann. Probab. 3, 534-545.
64. L. H. Y. Chen (1998) Stein’s method: some perspectives with applications. In: L. Accardi & C. C. Heyde (eds). Probability towards 2000. Lecture notes in statistics, Vol. 128, 97-122. Springer, New York.
65. L. H. Y. Chen & K. P. Choi (1990) Some asymptotic and large deviation results in Poisson approximation. Ann. Probab. 20, 1867-1876.
66. D. J. Daley & D. Vere-Jones (1988) An introduction to the theory of point processes. Springer, New York.
67. P. Deheuvels & D. Pfeifer (1988) On a relationship between Uspensky’s theorem and Poisson approximations. Ann. Inst. Statist. Math. 40, 671-681.
68. T. Erhardsson (1999) Compound Poisson approximation for Markov chains using Stein’s method. Ann. Probab. 27, 565-596.
69. T. Erhardsson (2000) Compound Poisson approximation for counts of rare patterns in Markov chains and extreme sojourns in birth-death chains. Ann. Appl. Probab. 10, 573-591.
70. J. D. Esary, F. Proschan & D. W. Walkup (1967) Association of random variables, with applications. Ann. Math. Statist. 38, 1466-1474.
71. S. Janson (1998) New versions of Suen’s correlation inequality. Random Structures Algorithms 13, 467-483.
72. K. Joag-Dev & F. Proschan (1983) Negative association of random variables, with applications. Ann. Statist. 11, 451-455.
73. J. Kerstan (1964) Verallgemeinerung eines Satzes von Prochorow und Le Cam. Z. Wahrsch. Verw. Gebiete 2, 173-179.
74. T. M. Liggett (1985) Interacting particle systems. Springer, New York.
75. R. Michel (1988) An improved error bound for the compound Poisson approximation of a nearly homogenous portfolio. Astin Bull. 17, 165-169.
76. M. Roos (1993) Stein-Chen method for compound Poisson approximation. PhD thesis, University of Zurich.
77. C. Stein (1972) A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. II: Probability theory, 583-602. Univ. California Press.
78. C. Stein (1986) Approximate computation of expectations. IMS Lecture Notes Vol. 7. Hayward, California.
79. D. J. Aldous (1989) Probability approximations via the Poisson clumping heuristic. Springer, New York.
80. P. K. Andersen, O. Borgan, R. D. Gill & N. Keiding (1993) Statistical Models Based on Counting Processes. Springer-Verlag, New York.
81. Barbour, A. D. (1988) Stein’s method and Poisson process convergence. J. Appl. Probab. 25(A), 175-184.
82. A. D. Barbour & T. C. Brown (1992a) Stein’s method and point process approximation. Stoch. Procs. Applies 43, 9-31.
83. A. D. Barbour & T. C. Brown (1992b) Stein-Chen method, point processes and compensators. Ann. Probab. 20, 1504-1527.
84. A. D. Barbour & T. C. Brown (1996) Approximate versions of Melamed’s theorem. J. Appl. Probab. 33, 472-489.
85. A. D. Barbour, T.C. Brown & A. Xia (1998) Point processes in time and Stein’s method. Stochastics and Stochastics Reports 65, 127-151.
86. A. D. Barbour & G. K. Eagleson (1983) Poisson approximation for some statistics based on exchangeable trials. Adv. Appl. Prob. 15, 585-600.
87. A. D. Barbour, L. Holst & S. Janson (1992) Poisson Approximation. Oxford Univ. Press.
88. A. D. Barbour & M. Mansson (2002) Compound Poisson process approximation. Ann. Probab. 30, 1492-1537.
89. P. Billingsley (1968) Convergence of probability measures. John Wiley & Sons.
90. T. C. Brown (1983) Some Poisson approximations using compensators. Ann. Probab. 11, 726-744.
91. T. C. Brown, M. Fackrell & A. Xia (2005) Poisson process approximation in Jackson networks. COSMOS 1 (to appear).
92. T. C. Brown & D. Greig (1994) Correction to: “Stein’s method and point process approximation” [Stoch. Procs Applies 43, 9-31 (1992)] by A. D. Barbour & T. C. Brown, Stoch. Procs. Applies 54, 291-296.
93. T. C. Brown & M. J. Phillips (1999) Negative Binomial Approximation with Stein’s Method. Methodology and Computing in Applied Probability 1, 407-421.
94. T. C. Brown, G. V. Weinberg & A. Xia (2000) Removing logarithms from Poisson process error bounds. Stoch. Procs. Applies 87, 149-165.
95. T.C. Brown & A. Xia (1995a) On metrics in point process approximation. Stochastics and Stoch. Reports 52, 247-263.
96. T. C. Brown & A. Xia (1995b) On Stein-Chen factors for Poisson approximation. Statis. Prob. Lett. 23, 327-332.
97. T. C. Brown & A. Xia (2001) Stein’s method and birth-death processes. Ann. Probab. 29, 1373-1403.
98. T. C. Brown & A. Xia (2002) How many processes have Poisson counts? Stock. Procs. Applies 98, 331-339.
99. L. H. Y. Chen (1975) Poisson approximation for dependent trials. Ann. Probab. 3, 534-545.
100. L. H. Y. Chen & A. Xia (2004) Stein’s method, Palm theory and Poisson process approximation. Ann. Probab. 32, 2545-2569.
101. D. R. Cox & V. Isham (1980) Point Processes. Chapman & Hall.
102. D. J. Daley & D. Vere-Jones (1988) An Introduction to the Theory of Point Processes. Springer-Ver lag, New York.
103. C. Dellacherie & P. A. Meyer (1982) Probabilities and Potential B. North-Holland.
104. W. Ehm (1991) Binomial approximation to the Poisson binomial distribution. Statistics and Probability Letters 11, 7-16.
105. S. N. Ethier & T. G. Kurtz (1986) Markov processes: characterization and convergence. John Wiley & Sons.
106. G. S. Fishman (1996) Monte Carlo, concepts, algorithms and applications. Springer, New York.
107. P. Franken, D. König, U. Arndt & V. Schmidt (1982) Queues and Point Processes. John Wiley & Sons.
108. D. Freedman (1974) The Poisson approximation for dependent events. Ann. Probab. 2, 256-269.
109. J. Jacod & A. N. Shiryaev (1987) Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin.
110. L. Janossy (1950) On the absorption of a nucleón cascade. Proc. R. Irish Acad. Sei. Sec. A 53, 181-188.
111. Yu. M. Kabanov, R. S. Liptser & A. N. Shiryaev (1983) Weak and strong convergence of distributions of counting processes. Theor. Probab. Appl. 28, 303-335.
112. O. kallenberg (1976) Random Measures. Academic Press.
113. A. F. Karr (1986) Point Processes and Their Statistical inference. Marcel Dekker.
114. J. keilson (1979) Markov Chain Models - Rarity and Exponentiality. Springer-Verlag.
115. J. kerstan (1964) Verallgemeinerung eines Satzes von Prochorow und Le Cam. Z. Wahrsch. verw. Geb. 2, 173-179.
116. J. F. C. Kingman (1993) Poisson processes. Oxford Univ. Press.
117. M. Y. Leung, K. P. Choi, A. Xia & L. H. Y. Chen (2004) Nonrandom Clusters of Palindromes in Herpesvirus Genomes. Journal of Computational Biology (to appear).
118. M. N. M. van Lieshout (2000) Markov point processes and their applications. Imperial College Press.
119. R. S. Liptser & A. N. Shiryaev (1978) Statistics of Random Processes (II). Springer-Verlag.
120. B. Matern (1986) Spatial variation. 2nd edn, Lecture Notes in Statistics 36, Springer-Verlag.
121. B. Melamed (1979) Characterizations of Poisson traffic streams in Jackson queueing networks. Adv. Appl. Prob. 11, 422-438.
122. C. Palm (1943) Intensitâtsschwankungen im Fernsprechverkehr. Ericsson Techniks 44, 1-189.
123. D. PFEIFER (1987) On the distance between mixed Poisson and Poisson distributions. Statistics and Decisions 5, 367-379.
124. Yu. V. PROHOROV (1956) Convergence of random processes and limit theorems in probability theory. Theory Probab. Appl. 1, 157-214.
125. C. J. Preston (1975) Spatial birth-and-death processes. Bull. ISI 46, 371-391.
126. S. T. Rachev (1991) Probability metrics and the Stability of Stochastic Models. John Wiley & Sons.
127. R. D. Reiss (1993) A course on point processes. Springer, New York.
128. A. Renyi (1967) Remarks on the Poisson process. Stud. Sci. Math. Hun-gar. 5, 119-123.
129. B. Roos (1999) On the rate of multivariate Poisson convergence. J. Multivariate Anal. 69, 120-134.
130. D. Ruelle (1969) Statistical mechanics: Rigorous results. W. A. Benjamin.
131. R. J. serfling (1975) A general Poisson approximation theorem. Ann. Probab. 3, 726-731.
132. A. N. Shiryaev (1984) Probability (translated by R. P. Boas). SpringerVerlag.
133. A. Sokal (1989) Monte Carlo methods in statistical mechanics: foundations and new algorithms. Cours de troisième cycle de la physique en Suisse romande.
134. C. STEIN (1971) A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proc. Sixth Berkeley Symp. Math. Statist. Prob. 3, 583-602.
135. L. Tierney (1994) Markov chains for exploring posterior distributions. Ann. Statist. 22, 1701-1728.
136. T. Viswanathan (1992) Telecommunication switching systems and networks. Prentice-Hall of India.
137. Z. Wang & X. Yang (1992) Birth and death processes and Markov chains. Springer-Verlag.
138. A. Xia (1994) Poisson Approximations and Some Limit Theorems for Markov Processes. PhD thesis, University of Melbourne, Australia.
139. A. Xia (1997a) On the rate of Poisson process approximation to a Bernoulli process. J. Appl. Probab. 34, 898-907.
140. A. Xia (1997b) On using the first difference in Stein-Chen method. Ann. Appl. Probab. 7, 899-916.
141. A. Xia (1999) A probabilistic proof of Stein’s factors. J. Appl. Probab. 36, 287-290.
142. A. Xia (2000) Poisson approximation, compensators and coupling. Stoch. Analysis and Applies 18, 159-177.
143. N. YANNAROS (1991) Poisson approximation for random sums of Bernoulli random variables. Statist. Probab. Lett. 11, 161-165.
144. R. Arratia, L. Goldstein & L. Gordon (1989) Two moments suffice for Poisson approximations: the Chen-Stein method. Ann. Probab. 17, 9-25.
145. N. T. J. Bailey (1975) The mathematical theory of infectious diseases and its applications. (2nd ed.) Griffin, London.
146. A. D. Barbour (1974) On a functional central limit theorem for Markov population processes. Adv. Appl. Probab. 6, 21-39.
147. A. D. Barbour (1975) The duration of the closed stochastic epidemic. Biometrika 62, 477-482.
148. A. D. Barbour (1988) Stein’s method and Poisson process convergence. J. Appl. Probab. 25A, 175-184.
149. A. D. Barbour (1990) Stein’s method for diffusion approximations. Probability Theory and Related Fields 84, 297-322.
150. A. D. Barbour, L. Holst & S. Janson (1992) Poisson Approximation. Oxford Science Publications.
151. M. S. Bartlett (1949) Some evolutionary stochastic processes. J. Roy. Statist. Soc., Ser. B 11, 211-229.
152. T. C. Brown & A. Xia (2001) Stein’s method and birth-death processes. Ann. Probab. 29, 1373-1403.
153. L. H. Y. Chen (1975) Poisson approximation for dependent trials. Ann. Probab. 3, 534-545.
154. P. Diaconis (1989) An example for Stein’s method. Stanford Stat. Dept. Technical Report.
155. P. Diaconis (2004) Stein’s method for Markov chains: first examples. In: Stein’s Method: Expository Lectures and Applications, Eds: P. Diaconis & S. Holmes, pp. 27-43. IMS Lecture Notes 46, Beachwood, Ohio.
156. P. Diaconis & S. Zabell (1991) Closed form summation for classical distributions: variations on a theme of de Moivre. Statistical Science 6, 284-302.
157. P. Eichelsbacher & G. Reinert (2004a) Stem’s method for discrete Gibbs measures. (In revision).
158. P. Eichelsbacher & G. Reinert (2004b) Stein’s method for spatial Gibbs measures. Preprint.
159. W. Ehm (1991) Binomial approximation to the Poisson binomial distribution. Statist. Probab. Lett. 11, 7-16.
160. S. N. Ethier & T. G. Kurtz (1986) Markov Processes, Characterization and Convergence. Wiley, New York.
161. L. Goldstein & G. Reinert (1997) Stein’s method and the zero bias transformation with application to simple random sampling. Ann. Appl. Probab. 7, 935-952.
162. L. Goldstein & G. Reinert (2005) Distributional transformations, orthogonal polynomials, and Stein characterizations. J. Theor. Probab. (to appear).
163. L. Goldstein & Y. Rinott (1996) On multivariate normal approximations by Stein’s method and size bias couplings. J. Appl. Prob. 33, 1-17.
164. F. Götze (1991) On the rate of convergence in the multivariate CLT. Ann. Probab. 19, 724-739.
165. S. Holmes (2004) Stein’s method for birth and death chains. In: Stein’s Method: Expository Lectures and Applications, Eds: P. Diaconis & S. Holmes, pp. 45-67. IMS Lecture Notes 46, Beachwood, Ohio.
166. O. Kallenberg (2002) Foundations of Modern Probability, 2nd edn. Springer, New York.
167. H.-R. künsch (1998) Personal communication.
168. H. M. Luk (1994) Stein’s method for the gamma distribution and related statistical applications. Ph.D. thesis, University of Southern California, Los Angeles, USA.
169. P. Massart (1990). The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality. Ann. Probab. 18, 1269-1283.
170. E. Peköz (1996) Stein’s method for geometric approximation. J. Appl. Probab. 33, 707-713.
171. A. pickett (2002) Stein’s method for chisquare approximations. Transfer thesis, University of Oxford.
172. A. Pickett & G. Reinert (2004) Stein’s method for chi-squared approximations. Preprint.
173. G. reinert (1994) A weak law of large numbers for empirical measures via Stein’s method. Ann. Probab. 23, 334-354.
174. G. Reinert (1995) The asymptotic evolution of the General Stochastic Epidemic. Ann. Appl. Probab. 5, 1061-1086.
175. G. REINERT (2001) Stein’s method in application for epidemic processes. In Complex Stochastic Systems, Eds: O. E. Barndorff-Nielsen, D. R. Cox & C. Kliippelberg, pp. 235-275. Chapman and Hall, Boca Raton.
176. G. Reinert & W. Schoutens (1998) Stein’s method for the hypergeometric distribution. Preprint.
177. −1/2 log n rate and applications to multivariate graph related statistics. J. Multivariate Analysis 56, 333-350.
178. W. Schoutens (2000) Stochastic Processes and Orthogonal Polynomials. Springer, New York.
179. T. Sellke (1983) On the asymptotic distribution of the size of a stochastic epidemic. J. Appl. Probab. 20, 390-394.
180. C. Stein (1986) Approximate Computation of Expectations. IMS, Hayward, California.
181. C. Stein, with P. Diaconis, S. Holmes & G. Reinert (2004) Use of exchangeable pairs in the analysis of simulations. In: Stein’s Method: Expository Lectures and Applications, Eds: P. Diaconis & S. Holmes, pp. 1-26. IMS Lecture Notes 46, Beachwood, Ohio.
182. A. W. Van der Vaart & J. A. Wellner (1996) Weak Convergence and Empirical Processes. Springer, New York.
183. F. S. J. Wang (1975) Limit theorems for age and density dependent stochastic population models. J. Math. Bio. 2, 373-400.
184. F. S. J. Wang (1977) A central limit theorem for age-and-density-dependent population processes. Stoch. Proc. Appl. 5, 173-193.
185. G. V. Weinberg (2000) Stein factor bounds for random variables. J. Appl. Probab. 37, 1181-1187.