Finite sample penalization in adaptive density deconvolution

Details Finite sample penalization in adaptive density deconvolution Finite sample penalization in adaptive density deconvolution

2006-01-05

arxiv.org/abs/math/0601098v1

Journal of Statistical Computation and Simulation 77, 11 (2007) 977-1000

Mathematics

Statistics Theory

Scientific paper

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.

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