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
收藏
页码：571 / 597
页数：27
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