Adaptive global thresholding on the sphere

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• 作者：Claudio Durastanti ^{claudio.durastanti@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62G08 ; 62G20 ; 65T60
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：151
• 期：Complete
• 页码：110-132
• 全文大小：622 K

文摘

This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the d$d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of spherical wavelets, the so-called needlets, which enjoy strong concentration properties in both harmonic and real domains. The author establishes the convergence rates of the L^p$L^p$-risks of these estimators, focusing on their minimax properties and proving their optimality over a scale of nonparametric regularity function spaces, namely, the Besov spaces.