Density estimation for RWRE
| Autor: | Matthieu Lerasle, Antoine Havet, Eric Moulines |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Estimator Mathematics - Statistics Theory 020206 networking & telecommunications 02 engineering and technology Density estimation Statistics Theory (math.ST) Random walk 01 natural sciences Oracle 010104 statistics & probability Uniform norm Distribution (mathematics) 0202 electrical engineering electronic engineering information engineering Trajectory FOS: Mathematics Applied mathematics Transient (computer programming) 0101 mathematics Statistics Probability and Uncertainty Mathematics |
| DOI: | 10.48550/arxiv.1806.05839 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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