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Article Dans Une Revue Canadian Journal of Statistics Année : 2006

Penalized contrast estimator for adaptive density deconvolution

Fabienne Comte
Yves Rozenholc
Marie-Luce Taupin

Résumé

The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X_i$, from a sample $Z_1, \dots, Z_n$ where $Z_i=X_i+\sigma\varepsilon_i$, $i=1, \dots, n$, $\varepsilon$ is a noise independent of $X$, with $\sigma\varepsilon$ 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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Dates et versions

hal-00016489 , version 1 (05-01-2006)

Identifiants

Citer

Fabienne Comte, Yves Rozenholc, Marie-Luce Taupin. Penalized contrast estimator for adaptive density deconvolution. Canadian Journal of Statistics, 2006, 34 (3), pp.431-452. ⟨10.1002/cjs.5550340305⟩. ⟨hal-00016489⟩
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