























Abstract:This paper addresses the nonparametric estimation of a spatially varying, heteroskedastic variance function on the unit sphere within a regression framework. While adaptive regression estimation is well-established on manifolds, characterizing localized noise structures presents unique theoretical obstacles due to bias propagation from the unknown mean function. To circumvent this, we propose a fully data-driven, multiresolution estimator based on localized spherical frames, namely, needlets, combined with a hard-thresholding protocol and a sample-splitting scheme. The approach exploits the excellent spatial and frequency localization properties of needlets to adaptively capture the local features of the variance function. We prove that the proposed estimator achieves the minimax-optimal rate of convergence over spherical Besov spaces under standard loss functions, exhibiting spatial adaptivity without requiring prior knowledge of the regularity of the variance function. This adaptivity highlights the efficacy of the method in analyzing spherical data characterized by complex heteroskedastic errors, with potential applications in fields such as cosmology, environmental modeling, and geophysics
From: Claudio Durastanti Prof. [view email]
[v1]
Wed, 7 Jan 2026 13:41:39 UTC (49 KB)
[v2]
Tue, 14 Jul 2026 17:17:26 UTC (2,900 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。