Efficient semiparametric estimator for heteroscedastic partially linear models

• 成果类型: Article
• 署名作者: Ma, Y; Chiou, JM; Wang, N
• 署名单位: Texas A&M University System; Texas A&M University College Station; Academia Sinica - Taiwan
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/93.1.75
• 发表日期: 2006
• 页码: 7584
• 关键词: Kernel; regression; splines

摘要

We study the heteroscedastic partially linear model with an unspecified partial baseline component and a nonparametric variance function. An interesting finding is that the performance of a naive weighted version of the existing estimator could deteriorate when the smooth baseline component is badly estimated. To avoid this, we propose a family of consistent estimators and investigate their asymptotic properties. We show that the optimal semiparametric efficiency bound can be reached by a semiparametric kernel estimator in this family. Building upon our theoretical findings and heuristic arguments about the equivalence between kernel and spline smoothing, we conjecture that a weighted partial-spline estimator could also be semiparametric efficient. Properties of the proposed estimators are presented through theoretical illustration and numerical simulations.