Finite sample penalization in adaptive density deconvolution. - Archive ouverte HAL
Article Dans Une Revue Journal of Statistical Computation and Simulation Année : 2007

Finite sample penalization in adaptive density deconvolution.

Fabienne Comte
Yves Rozenholc
Marie-Luce Taupin

Résumé

We consider the problem of estimating the density $g$ of identically distributed variables $X_i$, from a sample $Z_1, \dots, Z_n$ where $Z_i=X_i+\sigma\varepsilon_i$, $i=1, \dots, n$ and $\sigma \varepsilon_i$ is a noise independent of $X_i$ with known density $ \sigma^{-1}f_\varepsilon(./\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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Dates et versions

hal-00016503 , version 1 (05-01-2006)

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Fabienne Comte, Yves Rozenholc, Marie-Luce Taupin. Finite sample penalization in adaptive density deconvolution.. Journal of Statistical Computation and Simulation, 2007, 77 (11), pp.977-1000. ⟨hal-00016503⟩
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