Adaptive estimation of the transition density of a Markov chain

被引：15

作者：

Lacour, Claire ^{[1
]}

机构：

[1] Univ Paris 05, Lab MAP5, F-75270 Paris, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2007年 / 43卷 / 05期

关键词：

adaptive estimation; transition density; Markov chain; model selection; penalized contrast;

D O I：

10.1016/j.anihpb.2006.09.003

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：

In this paper a new estimator for the transition density pi of an homogeneous Markov chain is considered. We introduce an original contrast derived from regression framework and we use a model selection method to estimate pi under mild conditions. The resulting estimate is adaptive with an optimal rate of convergence over a large range of anisotropic Besov spaces B-2,B-infinity ((alpha 1, alpha 2)). Some simulations are also presented. (c) 2006 Elsevier Masson SAS. All rights reserved.

引用

页码：571 / 597

页数：27

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