On a Plug-In Wavelet Estimator for Convolutions of Densities

Abstract

The nonparametric estimation of the m-fold convolution power of an unknown function f is considered. We introduce an estimator based on a plug-in approach and a wavelet hard thresholding estimator. We explore its theoretical asymptotic performances via the mean integrated squared error, assuming that f has a certain degree of smoothness. Applications and numerical examples are given for the standard density estimation problem and the deconvolution density estimation problem.

AMS Subject Classification:

• 62G07
• 62G20

Keywords:

• Density estimation
• Convolutions
• Plug-in estimator
• Wavelets
• Hard thresholding
• Rates of convergence

Acknowledgment

We thank Jalal Fadili for his suggestions, which led to an improved version of the article.

Funding

This work is supported by ANR grant NatImages, ANR-08-EMER-009.