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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
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