Rates of convergence for the maximum likelihood estimator in mixture models

Journal of Nonparametric Statistics

Volumn 6, Issue 4, 1996, Pages 293-310

  Van De Geer, Sara ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Convex hull; Entropy; Hellinger distance; Maximum likelihood; Mixture model; Rate of convergence

Indexed keywords

EID: 0000073296     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485259608832677     Document Type: Article

References (16)

1. Ball, K. and Pajor, A. (1990). The entropy of convex bodies with "few" extreme points. Proceedings of the 1989 Conf. in Banach Spaces at Strobl. Austria. Cambridge Univ Press.
2. Birgé, L. and Massart, P. (1993). Rates of convergence for minimum contrast estimators. Prob. Theory and Rel. Fields 97, 113-150.
3. p. Mat. Sb. 73, 295-317.
4. Groeneboom, P. (1985). Estimating a monotone density. In Proc. Berkeley Conf. In Honor of Jerzy Neyman and Jack Kiefer 2 (L. LeCam and R. A. Olshen, eds.) 539-555. Univ. California Press, Berkeley.
5. Groeneboom, P. and Wellner, J. A. (1992). Information Bounds and Nonparametric Maximum Likelihood Estimation. DMV Seminar, Band 19, Birkhäuser, Basel, etc.
6. Ibragimov, I. A. and Has'minskii, R. Z. (1981). Statistical Estimation: Asymptotic Theory. Springer, New York.
7. Ledoux, M. and Talagrand, M. (1991). Probability in Banach Spaces. Springer, New York.
8. Pollard, D. (1984). Convergence of Stochastic Processes. Springer, New York.
9. Pollard, D. (1990). Empirical Processes: Theory and Applications. Siam, Philadelphia.
10. Prakasa Rao, B. L. S. (1969). Estimation of a unimodal density. Sankȳa Ser. A 31, 23-36.
11. Van De Geer, S. (1990). Estimating a regression function. Ann. Statist. 18, 907-924.
12. Van De Geer, S. (1993). Hellinger-consistency of certain nonparametric maximum likelihood estimators. Ann. Statist. 21 14-44.
13. Van De Geer, S. (1995). The method of sieves and minimum contrast estimators Math. Methods of Statistics 4, 20-38.
14. Van De Geer, S. (1994). Asymptotic normality in mixture models. Techn. Report TW 94-03, University of Leiden. To appear in: ESAIM: Probab. and statist. http: //www.emath.fr/ps/.
15. Wegkamp, M. H. (1994). Exponential bounds with applications to non-parametric regression and non-parametric density estimation. Techn. Report TW 94-08, University of Leiden.
16. Wong, W. H. and Shen, X. (1995). Probability inequalities for likelihood ratios and convergence rates for sieve MLEs. Ann. Statist. 23, 339-362.