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Penalized contrast estimator for adaptive density deconvolution. (English) Zbl 1104.62033
Summary: The authors consider the problem of estimating the density $$g$$ of independent and identically distributed variables $$X_i$$, from a sample $$Z_1,\dots,Z_n$$, such that $$Z_i = X_i + \sigma\varepsilon_i$$ for $$i = 1,\dots,n$$, and $$\varepsilon$$ is noise independent of $$X$$, with $$\sigma\varepsilon$$ having a known distribution. They present a model selection procedure allowing one to construct an adaptive estimator of $$g$$ and to find nonasymptotic risk bounds. The estimator achieves the minimax rate of convergence, in most cases where lower bounds are available. A simulation study gives an illustration of the good practical performance of the method.

##### MSC:
 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference
##### Keywords:
minimum contrast; estimators
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##### References:
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