The bernstein-von Mises theorem for the proportional hazard model

Annals of Statistics

Volumn 34, Issue 4, 2006, Pages 1678-1700

  Kim, Yongdai ^a  

^a Seoul National University   (South Korea)

Author keywords

Bernstein von Mises theorem; Neutral to the right process; Proportional hazard model

Indexed keywords

EID: 33845333028     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000000533     Document Type: Article

References (25)

1. BARRON, A., SCHERVISH, M. J. and WASSERMAN, L. (1999). The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 536-561. MR1714718
2. COX, D. D. (1993). An analysis of Bayesian inference for nonparametric regression. Ann. Statist. 21 903-923. MR1232525
3. COX, D. R. (1972). Regression models and life-tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187-220. MR0341758
4. DIACONIS, P. and FREEDMAN, D. (1986). On the consistency of Bayes estimates (with discussion). Ann. Statist. 14 1-67. MR0829555
5. DOKSUM, K. (1974). Tailfree and neutral random probabilities and their posterior distributions. Ann. Probab. 2 183-201. MR0373081
6. FERGUSON, T. S. and PHADIA, E. G. (1979). Bayesian nonparametric estimation based on censored data. Ann. Statist. 7 163-186. MR0515691
7. FREEDMAN, D. (1999). On the Bernstein-von Mises theorem with infinite-dimensional parameters. Ann. Statist. 27 1119-1140. MR1740119
8. GHOSAL, S., GHOSH, J. K. and RAMAMOORTHI, R. V. (1999). Consistency issues in Bayesian nonparametrics. In Asymptotics, Nonparametrics and Time Series (S. Ghosh, ed.) 639-667. Dekker, New York. MR1724711
9. GHOSAL, S., GHOSH, J. K. and VAN DER VAART, A. W. (2000). Convergence rates of posterior distributions. Ann. Statist. 28 500-531. MR1790007
10. HJORT, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Ann. Statist. 18 1259-1294. MR1062708
11. KALBFLEISCH, J. D. (1978). Non-parametric Bayesian analysis of survival time data. J. Roy. Statist. Soc. Ser. B 40 214-221. MR0517442
12. KIM, Y. (1999). Nonparametric Bayesian estimators for counting processes. Ann. Statist. 27 562-588. MR1714717
13. KIM, Y. and LEE, J. (2001). On posterior consistency of survival models. Ann. Statist. 29 666-686. MR1865336
14. KIM, Y. and LEE, J. (2003). Bayesian analysis of proportional hazard models. Ann. Statist. 31 493-511. MR1983539
15. KIM, Y. and LEE, J. (2003). Bayesian bootstrap for proportional hazards models. Ann. Statist. 31 1905-1922. MR2036394
16. KIM, Y. and LEE, J. (2004). A Bernstein-von Mises theorem in the nonparametric right-censoring model. Ann. Statist. 32 1492-1512. MR2089131
17. LAUD, P. W., DAMIEN, P. and SMITH, A. F. M. (1998). Bayesian nonparametric and covariate analysis of failure time data. Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statist. 133 213-225. Springer, New York. MR1630083
18. LEE, J. and KIM, Y. (2004). A new algorithm to generate beta processes. Comput. Statist. Data Anal. 47 441-453. MR2100560
19. Lo, A. Y. (1982). Bayesian nonparametric statistical inference for Poisson point processes. Z. Wahrsch. Verw. Gebiete 59 55-66. MR0643788
20. POLLARD, D. (1984). Convergence of Stochastic Processes. Springer, New York. MR0762984
21. SETHURAMAN, J. (1961). Some limit theorems for joint distributions. Sankhyā Ser. A 23 379-386. MR0139190
22. SHEN, X. (2002). Asymptotic normality of semiparametric and nonparametric posterior distributions. J. Amer. Statist. Assoc. 97 222-235. MR1947282
23. SHEN, X. and WASSERMAN, L. (2001). Rates of convergence of posterior distributions. Ann. Statist. 29687-714. MR1865337
24. TSIATIS, A. A. (1981). A large sample study of Cox's regression model. Ann. Statist. 9 93-108. MR0600535
25. ZHAO, L. H. (2000). Bayesian aspects of some nonparametric problems. Ann. Statist. 28 532-552. MR1790008