DATA-DRIVEN EFFICIENT ESTIMATORS FOR A PARTIALLY LINEAR-MODEL

• 成果类型: Article
• 署名作者: CHEN, H; SHIAU, JJH
• 署名单位: National Yang Ming Chiao Tung University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325366
• 发表日期: 1994
• 页码: 211-237
• 关键词: generalized cross-validation; Nonparametric Regression; spline; CONVERGENCE; rates

摘要

Chen and Shiau showed that a two-stage spline smoothing method and the partial regression method lead to efficient estimators for the parametric component of a partially linear model when the smoothing parameter is a deterministic sequence tending to zero at an appropriate rate. This paper is concerned with the large-sample behavior of these estimators when the smoothing parameter is chosen by the generalized cross validation (GCV) method or Mallows' C(L). Under mild conditions, the estimated parametric component is asymptotically normal with the usual parametric rate of convergence for both spline estimation methods. As a by-product, it is shown that the ''optimal rate' for the smoothing parameter, with respect to expected average squared error, is the same for the two estimation methods as it is for ordinary smoothing splines.