RWRE的密度估计

IF 0.8 Q3 STATISTICS & PROBABILITY

Mathematical Methods of Statistics Pub Date : 2019-05-03 DOI:10.3103/s1066530719010022

A. Havet, M. Lerasle, É. Moulines

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引用次数: 1

摘要

我们考虑了一个随机环境的非参数密度估计问题，该问题是通过观察随机行走的单个轨迹得到的。我们利用这个分布的矩建立了几个密度估计器。然后应用Goldenschluger-Lepski方法选择一个满足oracle型不等式的估计量。我们得到了当RWRE向右递归或暂态时，这些估计量的最大范数的非渐近界。一项模拟研究支持了我们的理论发现。

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Density Estimation for RWRE

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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来源期刊

Mathematical Methods of Statistics STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Mathematical Methods of Statistics is an is an international peer reviewed journal dedicated to the mathematical foundations of statistical theory. It primarily publishes research papers with complete proofs and, occasionally, review papers on particular problems of statistics. Papers dealing with applications of statistics are also published if they contain new theoretical developments to the underlying statistical methods. The journal provides an outlet for research in advanced statistical methodology and for studies where such methodology is effectively used or which stimulate its further development.