Adaptive global thresholding on the sphere

Claudio Durastanti

Journal of Multivariate Analysis, 2016, vol. 151, issue C, 110-132

Abstract: This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the 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 Lp-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.

Keywords: Global thresholding; Needlets; Spherical data; Nonparametric regression; U-statistics; Besov spaces; Adaptivity (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:151:y:2016:i:c:p:110-132

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DOI: 10.1016/j.jmva.2016.07.009

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