Optimal wavelet estimators of the heteroscedastic pointspread effects and Gauss white noises model

Jinru Wang, Wenhui Shi and Xiaochen Zeng

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 5, 1133-1154

Abstract: The problem of estimating a function’s derivative arises in many scientific settings, from medical imaging to astronomy. In this paper, we consider a hard thresholding wavelet approach to certain blind deconvolution problem based on the heteroscedastic data. Motivated by Delaigle & Meister’s work, the adaptive wavelet estimators are proposed and their asymptotic properties are investigated. It is shown that the derivative estimators for the blind deconvolution model are spatially adaptive and attain the optimal rate of convergence up to a logarithmic factor over a range of Besov classes. Our theorems generalize the results of Cai and Navarro et al. in some sense.

Date: 2022
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DOI: 10.1080/03610926.2020.1862874

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