Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7550453 | Stochastic Processes and their Applications | 2018 | 24 Pages |
Abstract
We investigate the problem of estimating the cumulative distribution function (c.d.f.) F of a distribution ν from the observation of one trajectory of the random walk in i.i.d. random environment with distribution ν on Z. We first estimate the moments of ν, then combine these moment estimators to obtain a collection of estimators (FÌnM)Mâ¥1 of F, our final estimator is chosen among this collection by Goldenshluger-Lepski's method. This estimator is easily computable. We derive convergence rates for this estimator depending on the Hölder regularity of F and on the divergence rate of the walk. Our rate is minimal when the chain realizes a trade-off between a fast exploration of the sites, allowing to get more information and a larger number of visits of each site, allowing a better recovery of the environment itself.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Roland Diel, Matthieu Lerasle,