Inhomogeneous and anisotropic conditional density estimation from dependent data

被引:14
作者
Akakpo, Nathalie [1 ]
Lacour, Claire [2 ]
机构
[1] Univ Paris 06, Lab Probabil & Modeles Aleatoires, F-75252 Paris, France
[2] Univ Paris 11, Fac Sci, Lab Math Orsay, F-91405 Orsay, France
来源
ELECTRONIC JOURNAL OF STATISTICS | 2011年 / 5卷
关键词
Conditional density; model selection; anisotropy; dependent data; adaptive estimation; NONPARAMETRIC-ESTIMATION; REGRESSION;
D O I
10.1214/11-EJS653
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
The problem of estimating a conditional density is considered. Given a collection of partitions, we propose a procedure that selects from the data the best partition among that collection and then provides the best piecewise polynomial estimator built on that partition. The observations are not supposed to be independent but only beta-mixing; in particular, our study includes the estimation of the transition density of a Markov chain. For a well-chosen collection of possibly irregular partitions, we obtain oracle-type inequalities and adaptivity results in the minimax sense over a wide range of possibly anisotropic and inhomogeneous Besov classes. We end with a short simulation study.
引用
收藏
页码:1618 / 1653
页数:36
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