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On the effect of estimating the error density in nonparametric deconvolution. (English) Zbl 1003.62514
Summary: It is quite common in the statistical literature on nonparametric deconvolution to assume that the error density is perfectly known. Since this seems to be unrealistic in many practical applications, we study the effect of estimating the unknown error density. We derive minimax rates of convergence and propose a modification of the usual kernel-based estimation scheme, which takes the uncertainty about the error density into account. A simulation study quantifies the possible gains by this new method in finite sample situations.

MSC:
62G07 Density estimation
Software:
KernSmooth
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