Asymptotic inference for mixture models using data-dependent priors

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 62, Issue 1, 2000, Pages 159-180

  Wasserman, Larry ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Coverage; Mixtures; Non informative priors

Indexed keywords

EID: 0034360396     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00226     Document Type: Article

References (31)

1. Chen, J. (1995) Optimal rate of convergence for finite mixture models. Ann. Statist., 23, 221-233.
2. Clarke, B. and Barron, A. (1994) Jeffreys' prior is asymptotically least favorable under entropy risk. J. Statist. Planng Inf., 41, 37-60.
3. Dacunha-Castelle, D. and Gassiat, E. (1997) Testing in locally conic models. Eur. Ser. Appl. Indust. Math. Probab. Statist., 1, 285-317.
4. Diebolt, J. and Robert, C. P. (1994) Estimation of finite mixture distributions through Bayesian sampling. J. R. Statist. Soc. B, 56, 363-375.
5. Escobar, M. and West, M. (1995) Bayesian density estimation and inference using mixtures. J. Am. Statist. Ass., 90, 577-588.
6. Garel, B. (1998) Asymptotic theory of the likelihood ratio test for the identification of a mixture. Research Report 05-98. ENSEEIHT, Toulouse.
7. Geman, S. and Huang, C. (1982) Nonparametric maximum likelihood estimation by the method of sieves. Ann. Statist., 10, 401-414.
8. Genovese, C. and Wasserman, L. (1998) Rates of convergence of the Gaussian mixture sieve. Technical Report 685. Department of Statistics, Carnegie Mellon University, Pittsburgh.
9. Ghoshal, S., Ghosh, J. K. and Ramamoorthi, R. V. (1997) Non-informative priors via sieves and packing numbers. Unpublished.
10. Grenander, U. (1981) Abstract Inference. New York: Wiley.
11. Hartigan, J. (1983) Bayes Theory. New York: Springer.
12. Jeffreys, H. (1961) Theory of Probability, 3rd edn. Oxford: Clarendon.
13. Kass, R. E. and Wasserman, L. (1996) The selection of prior distributions by formal rules. J. Am. Statist. Ass., 91, 1343-1370.
14. Keribin, C. (1998) Consistent estimation of the order of mixture models. Technical Report. Laboratoire Analyse et Probabilité, Université d'Evry-Val d'Essonne.
15. Lindsay, B. (1995) Mixture models: theory, geometry and applications. Regl Conf. Ser. Probab. Statist., 5.
16. MacEachern, S. and Mueller, P. (1995) Estimating mixture of Dirichlet process models. Technical Report. Ohio State University, Columbus.
17. Marron, J. S. and Wand, M. P. (1992) Exact mean integrated squared error. Ann. Statist., 20, 712-736.
18. Mengersen, K. and Robert, C. (1996) Testing for mixtures: a Bayesian entropie approach. In Bayesian Statistics 5 (eds J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), pp. 255-276. Oxford: Clarendon.
19. Nicolaou, A. (1993) Bayesian intervals with good frequentist behaviour in the presence of nuisance parameters. J. R. Statist. Soc. B, 55, 377-390.
20. Nobile, A. (1994) Bayesian analysis of finite mixture distributions. PhD Dissertation. Department of Statistics, Carnegie Mellon University, Pittsburgh.
21. Policello, G. (1981) Conditional maximum likelihood estimation in Gaussian mixtures. In Statistical Distributions in Scientific Work, vol. 5, pp. 111-125.
22. Raftery, A. E. (1996) Hypothesis testing and model selection via posterior simulation. In Practical Markov Chain Monte Carlo (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter), pp. 163-188. London: Chapman and Hall.
23. Richardson, S. and Green, P. J. (1997) On Bayesian analysis of mixtures with an unknown number of components (with discussion). J. R. Statist. Soc. B, 59, 731-792.
24. Roeder, K. (1992) Semiparametric estimation of normal mixture densities. Ann. Statist., 20, 929-943.
25. Roeder, K. and Wasserman, L. (1997) Practical Bayesian density estimation using mixtures of normals. J. Am. Statist. Ass., 92, 894-902.
26. Sethuraman, J. (1994) A constructive definition of Dirichlet priors. Statist. Sin., 4, 639-650.
27. Tierney, L. and Kadane, J. (1986) Accurate approximations for posterior moments and marginal densities. J. Am. Statist. Ass., 81, 82-86.
28. van der Vaart, A. and Wellner, J. (1996) Weak Convergence and Empirical Processes. New York: Springer.
29. Verdinelli, I. and Wasserman, L. (1991) Bayesian analysis of outlier problems using the Gibbs sampler. Statist. Comput., 1, 105-117.
30. Welch, B. L. and Peers, H. W. (1963) On formulae for confidence points based on integrals of weighted likelihoods. J. R. Statist. Soc. B, 25, 318-329.
31. Wong, W. and Shen, X. (1995) Probability inequalities for likelihood ratios and convergence rates of sieve MLE's. Ann. Statist., 23, 339-362.