Density Estimation for RWRE

A. Havet; M. Lerasle

doi:10.3103/S1066530719010022

Density Estimation for RWRE

A. Havet
, M. Lerasle
, Moulines

Université Paris-Saclay

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	18-38
Number of pages	21
Journal	Mathematical Methods of Statistics
Volume	28
Issue number	1
DOIs	https://doi.org/10.3103/S1066530719010022
Publication status	Published - 1 Jan 2019
Externally published	Yes

Keywords

adaptive estimation
nonparametric density estimation
oracle inequality
random walk in random environment

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title = "Density Estimation for RWRE",

abstract = "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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AU - Lerasle, M.

AU - Moulines,

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Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - adaptive estimation

KW - nonparametric density estimation

KW - oracle inequality

KW - random walk in random environment

U2 - 10.3103/S1066530719010022

DO - 10.3103/S1066530719010022

M3 - Article

AN - SCOPUS:85065259957

SN - 1066-5307

VL - 28

SP - 18

EP - 38

JO - Mathematical Methods of Statistics

JF - Mathematical Methods of Statistics

IS - 1

ER -

Density Estimation for RWRE

Abstract

Keywords

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