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Density Estimation for RWRE

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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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Authors and Affiliations

  1. Centre de Math. Appl., École polytech., CNRS Univ. Paris-Saclay, Paris, France

    A. Havet & É. Moulines

  2. Laborat. Math. d’Orsay, Univ. Paris-Sud, CNRS Univ. Paris-Saclay, Paris, France

    M. Lerasle

Authors
  1. A. Havet
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  2. M. Lerasle
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  3. É. Moulines
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Corresponding authors

Correspondence to A. Havet, M. Lerasle or É. Moulines.

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Havet, A., Lerasle, M. & Moulines, É. Density Estimation for RWRE. Math. Meth. Stat. 28, 18–38 (2019). https://doi.org/10.3103/S1066530719010022

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  • DOI: https://doi.org/10.3103/S1066530719010022

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