Wavelet thresholding for nonnecessarily Gaussian noise: Functionality

• 成果类型: Article
• 署名作者: Averkamp, R; Houdré, C
• 署名单位: University of Freiburg; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000471
• 发表日期: 2005
• 页码: 2164-2193
• 关键词: spatial adaptation; shrinkage; estimators

摘要

For signals belonging to balls in smoothness classes and noise with enough moments, the asymptotic behavior of the minimax quadratic risk among soft-threshold estimates is investigated. In turn, these results, combined with a median filtering method, lead to asymptotics for denoising heavy tails via wavelet thresholding. Some further comparisons of wavelet thresholding and of kernel estimators are also briefly discussed.