Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors

• 成果类型: Article
• 署名作者: Lepski, OV; Mammen, E; Spokoiny, VG
• 署名单位: Federal Research Center Computer Science & Control of RAS; Institute Systems Analysis of Russian Academy of Sciences; Ruprecht Karls University Heidelberg; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 929-947
• 关键词: white-noise; Nonparametric Regression; asymptotic equivalence; DENSITY-ESTIMATION; wavelet shrinkage

摘要

A new variable bandwidth selector for kernel estimation is proposed. The application of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over Besov classes. This implies that the procedure adapts to spatially inhomogeneous smoothness. In particular, the estimates share optimality properties with wavelet estimates based on thresholding of empirical wavelet coefficients.