数学物理学报(英文版)

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EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

张日权; 李国英   

  1. 山西大同大学数学系, 大同 037009
  • 收稿日期:2005-05-08 修回日期:2006-10-29 出版日期:2008-10-20 发布日期:2008-10-20
  • 通讯作者: 张日权
  • 基金资助:

    The research was supported by the Shanxi Natural Science Foundation (2007011014)

EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

Zhang Riquan; Li Guoying   

  1. 1.Department of Mathematics, Shanxi Datong University, Datong 037009, China; 2.Department of Statistics, East China Normal University, Shanghai 200062, China; 3.Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2005-05-08 Revised:2006-10-29 Online:2008-10-20 Published:2008-10-20
  • Contact: Zhang Riquan

摘要:

In this article, a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined. First step, by the local linear technique and the averaged method, the initial estimates of the coefficient functions are given. Second step, based on the initial estimates, the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure. The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions. Two simulated examples show that the procedure is effective.

关键词: Asymptotic normality, averaged method, different smoothing variables, functional-coefficient regression models, local linear method, one-step backfitting procedure

Abstract:

In this article, a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined. First step, by the local linear technique and the averaged method, the initial estimates of the coefficient functions are given. Second step, based on the initial estimates, the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure. The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions. Two simulated examples show that the procedure is effective.

Key words: Asymptotic normality, averaged method, different smoothing variables, functional-coefficient regression models, local linear method, one-step backfitting procedure

中图分类号: 

  • 62G08