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.
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.