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 Block thresholding for wavelet-based estimation of function derivatives from a heteroscedastic multichannel convolution model
 We observe $n$ heteroscedastic stochastic processes $\{Y_v(t)\}_{v}$, where for any $v\in\{1,\ldots,n\}$ and $t \in [0,1]$, $Y_v(t)$ is the convolution product of an unknown function $f$ and a known blurring function $g_v$ corrupted by Gaussian noise. Under an ordinary smoothness assumption on $g_1,\ldots,g_n$, our goal is to estimate the $d$-th derivatives (in weak sense) of $f$ from the observations. We propose an adaptive estimator based on wavelet block thresholding, namely the "BlockJS estimator". Taking the mean integrated squared error (MISE), our main theoretical result investigates the minimax rates over Besov smoothness spaces, and shows that our block estimator can achieve the optimal minimax rate, or is at least nearly-minimax in the least favorable situation. We also report a comprehensive suite of numerical simulations to support our theoretical findings. The practical performance of our block estimator compares very favorably to existing methods of the literature on a large set of test functions.
 Équipe de recherche : LMNOGREYCimage
 Mots Clés : deconvolution – multichannel observations – derivative estimation – wavelets – block thresholding – minimax
 hal-00661544, version 2 http://hal.archives-ouvertes.fr/hal-00661544 oai:hal.archives-ouvertes.fr:hal-00661544 Contributeur : Fabien Navarro <> Soumis le : Lundi 26 Mars 2012, 16:49:58 Dernière modification le : Lundi 26 Mars 2012, 19:45:41