Density Estimation for RWRE

被引：0
作者：
A. Havet
M. Lerasle
É. Moulines
机构：
[1] CNRS Univ. Paris-Saclay,Centre de Math. Appl., École polytech.
[2] Univ. Paris-Sud,Laborat. Math. d’Orsay
[3] CNRS Univ. Paris-Saclay,undefined
来源：
Mathematical Methods of Statistics | 2019年 / 28卷
关键词：
random walk in random environment; nonparametric density estimation; adaptive estimation; oracle inequality; primary 62G07; secondary 60K37; 62M05; 62E17;
D O I：
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中图分类号：
学科分类号：
摘要：
We consider the problem of nonparametric density estimation of a random environment from the observation of a single trajectory of a random walk in this environment. We build several density estimators using the beta-moments of this distribution. Then we apply the Goldenschluger-Lepski method to select an estimator satisfying an oracle type inequality. We obtain non-asymptotic bounds for the supremum norm of these estimators that hold when the RWRE is recurrent or transient to the right. A simulation study supports our theoretical findings.
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页码：18 / 38
页数：20
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