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Fast nonparametric estimation for convolutions of densities. (English. French summary) Zbl 1348.62119

Summary: This paper is concerned with the problem of estimating the convolution of densities. We propose an adaptive estimator based on kernel methods, Fourier analysis and the Lepski method. We study the \(\mathbb L_2\)-risk properties of the estimator. Fast and new rates of convergence are determined for a wide class of unknown functions. Numerical illustrations, on both simulated and real data, are provided to assess the performance of our procedure.

MSC:

62G07 Density estimation
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference

Software:

AS 176
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References:

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