Posterior consistency for some semi-parametric problems

Sankhya: The Indian Journal of Statistics

Volumn 70, Issue 2 SERIES A, 2008, Pages 267-313

  Wu, Yuefeng ^a   Ghosal, Subhashis ^b  

^a Cornell University ^*  (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Consistency; Exponentially consistent test; Exponentially frailty model; Generalized linear model; Kullback Leibler property; Multiple linear regression

Indexed keywords

EID: 76849111526     PISSN: 09727671     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. Amewou-Atisso, M., Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (2003). Posterior consistency for semi-parametric regression problems. Bernoulli 9, 291-312.
2. Barron, A., Schervis, M. and Wasserman, L. (1999). The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536-561.
3. Basu, S. and Mukhopadhyay, S. (2000). Binary response regression with normal scale mixtures links, In Generalized Linear Models: A Bayesian Perspective, (D. K. Dey, S. K. Ghosh, and B. K. Mallick, eds.) New York, Marcel Dekker.
4. Bickel, P. J., Klaassen, C. A. J., Ritov, Y. and Wellner, J. A. (1993). Efficient and adaptive estimation for semiparametric models. Johns Hopkins University Press, Baltimore.
5. Blasi, P. D., Peccati, G. and Prünster, I. (2009). Asymptiotics for posterior hazards. Ann. Statist. (to appear).
6. Cantor, A. B. and Knapp, R. G. (1985). A test of the equality of survival distributions based on paired observations from conditionally independent exponential distributions. IEEE Transactions on Reliability, 34 342-346.
7. Castillo, I. (2008). A semiparametric Bernstein-von Mises theorem. Preprint.
8. Choudhuri, N., Ghosal, S. and Roy, A. (2004). Bayesian estimation of the spectral density of a time series. J. Amer. Statist. Assoc. 99, 1050-1059.
9. Choudhuri, N., Ghosal, S. and Roy, A. (2005). Bayesian methods for function estimation. Handbook of Statistics, 25, (D. K. Dey and C. R. Rao, eds.) 373-414.
10. Cox, D. R. (1972). Regression models and life tables. J. Roy. Statist. Soc., Ser. B 34, 187-220.
11. Diaconis, P. and Freedman, D. (1986). On the consistency of Bayes estimates (with discussion). Ann. Statist. 14, 1-67.
12. Doob, J. L. (1948). Application of the theory of martingales. Coll. Int. du CNRS, Paris, 22-28.
13. Doss, H. (1985). Bayesian nonparametric estimation of the median. II: Asymptotic properties of the estimates. Ann. Statist. 13, 1445-1464.
14. Freedman, D. (1963). On the asymptotic distribution of Bayes estimates in the discrete case I. Ann. Math. Statist. 34, 1386-1403.
15. Freedman, D. (1965). On the asymptotic distribution of Bayes estimates in the discrete case II. Ann. Math. Statist. 36, 454-456.
16. Gelfand, A. E. and Kuo, L. (1991). Nonparametric Bayesian bioassay including ordered polytomous response. Biometrika 78, 657-666.
17. Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (1999a). Consistency issues in Bayesian nonparametrics. In Asymptotics, Nonparametrics and Time Series: A Tribute to Madan Lal Puri. (S. Ghosh ed.,) Marcel Dekker, New York, 639-668.
18. Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (1999b). Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27143-158.
19. Ghosal, S. (2009). Dirichlet process, related priors and posterior asymptotics. In Bayesian Nonparametrics in Practice (Hjort, N. L., et al., eds.) Cambridge University Press (to appear).
20. Ghosh, J. K. and Ramamoorthi, R. V. (2003). Bayesian Nonparametrics. Springer-Verlag, New York.
21. Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13-30.
22. Kim, Y. (2006). The Bernstein-von Mises theorem for the proportional hazard model. Ann. Statist. 34, 1678-1700.
23. Mallick, B. K. and Gelfand, A. E. (1994). Generalized linear models with unknown link functions. Biometrika 81 237-245.
24. Massey, F. J. (1951). The Kolmogorov-Smirnov test for goodness of fit. J. Amer. Statist. Assoc., 46 68-78.
25. Newton, M. A., Czado, C. and Chappell, R. (1996). Bayesian inference for semi-parametric binary regression. J. Amer. Statist. Assoc. 91, 142-153.
26. Schwartz, L. (1965). On Bayes procedures. Z. Wahsch. Verw. Gebiete 4 10-26.
27. Shen, X. (2002). Asymptotic normality of semiparametric and nonparametric posterior distributions. J. Amer. Statist. Assoc. 97, 222-235.
28. Tokdar, S. (2006). Posterior consistency of Dirichlet location-scale mixture of normals in density estimation and regression. Sankhya 67, 90-110.
29. van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes with Applications to Statistics. Springer-Verlag, New York.
30. Walker, S. G. (2004). New approaches to Bayesian consistency. Ann. Statist. 32, 2028-2043.
31. Wu, Y. and Ghosal, S. (2008). Kullback Leibler property of kernel mixture priors in Bayesian density estimation. Electronic J. Statist. 2, 298-331