Rates of convergence for the Gaussian mixture sieve

Annals of Statistics

Volumn 28, Issue 4, 2000, Pages 1105-1127

  Genovese, Christopher R ^a   Wasserman, Larry ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Density estimation; Mixtures; Rates of convergence; Sieves

Indexed keywords

EID: 0034237946     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015956709     Document Type: Article

References (20)

1. BANFIELD, J. and RAFTERY, A. (1993). Model-based Gaussian and non-Gaussian clustering. Biometrics 49 803-821.
2. BARRON, A. and YANG, Y. (1995). An asymptotic property of model selection criteria. Technical report, Dept. Statistics, Yale Univ.
3. CHEN, J. (1995). Optimal rate of convergence for finite mixtures models. Ann. Statist. 23 221-233.
4. ESCOBAR, M. and WEST, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 577-588.
5. GEMEN, S. and HWANG, C. (1982). Nonparametric maximum likelihood estimation by the method of sieves. Ann. Statist. 10 401-414.
6. GHOSAL, S. and VAN DER VAART, A. (2000). Rates of convergence for Bayes and maximum likelihood estimation for mixtures of normal densities. Unpublished manuscript.
7. GRENANDER, U. (1981). Abstract Inference. Wiley, New York.
8. HALL, P. (1987). On Kullback-Leibler loss and density estimation. Ann. Statist. 15 1491-1519.
9. LI, J. (1999). Estimation of mixtures models. Ph.D. dissertation, Dept. Statistics. Yale Univ.
10. LI, J. and BARRON, A. (1999). Mixture density estimation. Preprint.
11. LINDSAY, B. (1995). Mixture Models: Theory, Geometry and Applications. IMS, Hayward, CA.
12. MCLACHLAN, G. and BASFORD, K. (1988). Mixture Models: Inference and Applications to Clustering. Dekker, New York.
13. PRIEBE, C. (1994). Adaptive mixtures. J. Amer. Statist. Assoc. 89 796-806.
14. ROBERT, C. (1996). Mixtures of distributions: inference and estimation. In Markov Chain Monte Carlo in Practice (W. Gilks, S. Richardson, D Spiegelhalter, eds.) 441-464. Chapman and Hall, London.
15. ROEDER, K. and WASSERMAN, L. (1997). Practical Bayesian density estimation using mixtures of normals. J. Amer. Statist. Assoc. 92 894-902.
16. ROEDER, K. (1992). Semiparametric estimation of normal mixture densities. Ann. Statist. 20 929-943.
17. TONG, B., and VIELE, K. (1998). Mixtures of normal linear regressions. Technical report, Univ. Kentucky.
18. VAN DE GEER, S. (1996). Rates of convergence for the maximum likelihood estimator in mixture models. Nonparametric Statist. 6 293-310.
19. VAN DER VAART, A. and WELLNER, J. (1996). Weak Convergence and Empirical Processes. Springer, New York.
20. WONG, W. and SHEN, X. (1995). Probability inequalities for likelihood ratios and convergence rates of sieve MLEs. Ann. Statist. 23 339-362.