Variance estimation in nonparametric regression via the difference sequence method

• 成果类型: Article
• 署名作者: Brown, Lawrence D.; Levine, M.
• 署名单位: University of Pennsylvania; Purdue University System; Purdue University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000145
• 发表日期: 2007
• 页码: 2219-2232
• 关键词: square successive difference; residual variance; geometrizing rates; call center; heteroscedasticity; CONVERGENCE; DESIGN; models; CHOICE; ratio

摘要

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for suitable asymptotic formulations our estimators achieve the minimax rate.