Adaptive thresholding for wavelet-based nonparametric heteroskedastic variance estimation on the sphere

Abstract

This paper investigates the nonparametric estimation of a heteroskedastic variance function on the sphere in a regression framework, assuming the variance belongs to a Besov regularity class. A needlet-based estimator is proposed, combining multiresolution analysis with hard thresholding. The method exploits the spatial and spectral localization of needlets to adapt to unknown smoothness and is shown to attain minimax-optimal convergence rates over Besov spaces.