Penalized contrast estimator for adaptive density deconvolution

Details Penalized contrast estimator for adaptive density deconvolution Penalized contrast estimator for adaptive density deconvolution

2006-01-05

arxiv.org/abs/math/0601091v1

The Canadian Journal of Statistics / La Revue Canadienne de Statistique 34, 3 (2006) 431-452

Mathematics

Statistics Theory

Scientific paper

The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$, $\epsilon$ is a noise independent of $X$, with $\sigma\epsilon$ having known distribution. They present a model selection procedure allowing to construct an adaptive estimator of $g$ and to find non-asymptotic bounds for its $\mathbb{L}\_2(\mathbb{R})$-risk. The estimator achieves the minimax rate of convergence, in most cases where lowers bounds are available. A simulation study gives an illustration of the good practical performances of the method.

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