Adaptive wavelet estimator for nonparametric density deconvolution

• 成果类型: Article
• 署名作者: Pensky, M; Vidakovic, B
• 署名单位: State University System of Florida; University of Central Florida; Duke University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 2033-2053
• 关键词: multivariate densities; Asymptotic Normality; stationary-processes; curve estimation; Optimal Rates; CONVERGENCE; kernel; error

摘要

The problem of estimating a density g based on a sample X-1, X-2, X-n from p = q * g is considered. Linear and nonlinear wavelet estimators teased on Meyer-type wavelets are constructed. The estimators are asymptotically optimal and adaptive if g belongs to the Sobolev space H-alpha. Moreover, the estimators considered in this paper adjust automatically to the situation when g is supersmooth.