Data-driven wavelet estimations in the convolution structure density model

Abstract

<abstract><p>Based on a data-driven kernel estimator, Lepski and Willer considered the problem of adaptive $ L^{p} $ risk estimations in the convolution structure density model in 2017 and 2019. This current paper studies the same problem with a data-driven wavelet estimator on Besov spaces, as wavelet estimations offer fast algorithm and provide more local information. Our results can reduce to the traditional adaptive wavelet estimations in the classical density model with no errors, as well as deconvolutional model.</p></abstract>