The L1-consistency of Dirichlet mixtures in multivariate Bayesian density estimation

Journal of Multivariate Analysis

Volumn 101, Issue 10, 2010, Pages 2411-2419

  Wu, Yuefeng ^a   Ghosal, Subhashis ^b  

^a Department of Obstetrics Gynecology   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Density estimation; Dirichlet process; Kullback Leibler property; Mixture; Multivariate; Posterior consistency; Posterior distribution

Indexed keywords

EID: 77956773597     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2010.06.012     Document Type: Article

References (16)

1. A.R. Barron, The exponential convergence of posterior probabilities with implications for Bayes estimators of density functions, Technical Report 7, Dept. Statistics, Univ. Illinois, Champaign, 1988.
2. Ferguson T.S. A Bayesian analysis of some nonparametric problems. Ann. Statist. 1973, 1:209-230.
3. Fraley C., Raftery A.E. Model-based clustering, discriminant analysis, and density estimation. J. Amer. Statist. Assoc. 2002, 97:611-631.
4. Ghosal S., Ghosh J.K., Ramamoorthi R.V. Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 1999, 27:143-158.
5. Ghosal S., van der Vaart A.W. Entropies and rates of convergence for Bayes and maximum likelihood estimation for mixture of normal densities. Ann. Statist. 2001, 29:1233-1263.
6. Ghosal S., van der Vaart A.W. Posterior convergence rates of Dirichlet mixtures at smooth densities. Ann. Statist. 2007, 35:697-723.
7. Ghosh J.K., Ramamoorthi R.V Bayesian Nonparametrics 2003, Springer-Verlag, New York.
8. Lo A.Y. On a class of Bayesian nonparametric estimates I: density estimates. Ann. Statist. 1984, 12:351-357.
9. Müller P., Erkanli A., West M. Bayesian curve fitting using multivariate normal mixtures. Biometrika 1996, 83:67-79.
10. Ormoneit D., Tresp V. Improved Gaussian mixture density estimates using Bayesian penalty terms and network averaging. Advances in Neural Information Processing 1996, vol. 8:542-548. MIT Press.
11. Schwartz L. On Bayes procedures. Z. Wahrsch. Verw. Gebiete 1965, 4:10-26.
12. Tokdar S. Posterior consistency of Dirichlet location-scale mixture of normals in density estimation and regression. Sankhya 2006, 67:90-110.
13. Tyrtyshnikov E.E. A Brief Introduction to Numerical Analysis 1997, Birhäuser, Boston.
14. West M., Müller P., Escobar M.D. Hierarchical priors and mixture models, with applications in regression and density estimation. Aspects of Uncertainty: A Tribute to D.V. Lindley 1994, 363-386. Wiley, Chichester. P.R. Freeman, A.F.M. Smith (Eds.).
15. Woo Mi-Ja, Sriram T.N. Robust estimation of mixture complexity for count data. Computational Statistics & Data Analysis 2007, 51:4379-4392.
16. Wu Y., Ghosal S. Kullback-Leibler property of kernel mixture priors in Bayesian density estimation. Electronic J. Statist.. Correction: Electronic J. Statist. 2009, 3:316-317.