Finite sample penalization in adaptive density deconvolution

TL;DR

This paper develops and tests adaptive density estimators for deconvolution problems with known noise distribution, demonstrating their robustness and superior performance across various scenarios.

Contribution

It generalizes adaptive estimators using model selection for density deconvolution and evaluates their robustness and efficiency through numerical experiments.

Findings

Estimator performs well across different contexts

Robust to misspecification of errors

Outperforms traditional kernel estimators

Abstract

We consider the problem of estimating the density $g$ of identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$ and $\sigma \epsilon\_i$ is a noise independent of $X\_i$ with known density $ \sigma^{-1}f\_\epsilon(./\sigma)$. We generalize adaptive estimators, constructed by a model selection procedure, described in Comte et al. (2005). We study numerically their properties in various contexts and we test their robustness. Comparisons are made with respect to deconvolution kernel estimators, misspecification of errors, dependency,... It appears that our estimation algorithm, based on a fast procedure, performs very well in all contexts.