文章基本信息

标题：Efficient semiparametric estimation and model selection for multidimensional mixtures
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作者：Elisabeth Gassiat ; Judith Rousseau ; Elodie Vernet 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2018
卷号：12
期号：1
页码：703-740
DOI：10.1214/17-EJS1387
语种：English
出版社：Institute of Mathematical Statistics
摘要：In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components which are independent given the population. We approximate the semiparametric model by projecting the conditional distributions on step functions associated to some partition. Our first main result is that if we refine the partition slowly enough, the associated sequence of maximum likelihood estimators of the weights is asymptotically efficient, and the posterior distribution of the weights, when using a Bayesian procedure, satisfies a semiparametric Bernstein-von Mises theorem. We then propose a cross-validation like method to select the partition in a finite horizon. Our second main result is that the proposed procedure satisfies an oracle inequality. Numerical experiments on simulated data illustrate our theoretical results.