Adaptive Wavelet Estimations in the Convolution Structure Density Model

Kaikai Cao and Xiaochen Zeng
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Kaikai Cao: School of Mathematics and Information Science, Weifang University, Weifang 261061, China
Xiaochen Zeng: School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China

Mathematics, 2020, vol. 8, issue 9, 1-11

Abstract: Using kernel methods, Lepski and Willer study a convolution structure density model and establish adaptive and optimal L p risk estimations over an anisotropic Nikol’skii space (Lepski, O.; Willer, T. Oracle inequalities and adaptive estimation in the convolution structure density model. Ann. Stat. 2019 , 47 , 233–287). Motivated by their work, we consider the same problem over Besov balls by wavelets in this paper and first provide a linear wavelet estimate. Subsequently, a non-linear wavelet estimator is introduced for adaptivity, which attains nearly-optimal convergence rates in some cases.

Keywords: generalized deconvolution; adaptive density estimation; wavelet; Besov space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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