固定设计下一类半参数回归模型估计的强相合性

数学季刊 ›› 2006, Vol. 21 ›› Issue (2): 202-209.

固定设计下一类半参数回归模型估计的强相合性

College of Applied Sciences, Beijing University of Technology, Beijing 100022, China;Department of Mathematics, Xuchang University, Xuchang 461000, China

收稿日期:2005-05-19 出版日期:2006-06-30 发布日期:2023-12-05
作者简介:TlAN Ping(1971-),female,native of Xuchang,Henan,an associate professor of Xuchang University,Ph.D,engages in nonparametric statistics;XUE Liu-gen(1957-),male,native of Xuchang,Henan,a professor of Beijing University of Technology,engages in nonparametric statistics.
基金资助:
Supported by the National Natural Science Foundation of China(10571008)； Supported by the Natural Science Foundation of Henan(0511013300)； Supported by the National Science Foundation of Henan Education Department(2006110012)；

Strong Consistency of Estimators of a Semiparametric Regression Model under Fixed Design

College of Applied Sciences, Beijing University of Technology, Beijing 100022, China;Department of Mathematics, Xuchang University, Xuchang 461000, China

Received:2005-05-19 Online:2006-06-30 Published:2023-12-05
About author:TlAN Ping(1971-),female,native of Xuchang,Henan,an associate professor of Xuchang University,Ph.D,engages in nonparametric statistics;XUE Liu-gen(1957-),male,native of Xuchang,Henan,a professor of Beijing University of Technology,engages in nonparametric statistics.
Supported by:
Supported by the National Natural Science Foundation of China(10571008)； Supported by the Natural Science Foundation of Henan(0511013300)； Supported by the National Science Foundation of Henan Education Department(2006110012)；

摘要/Abstract

摘要： In this paper, we consider the following semiparametric regression model under fixed design: y_i=x_i¹β+g(x_i)+e_i. The estimators of β, g(·) and σ²are obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.

关键词: semiparametric , regression , model, least , square , estimation, weight , function, strong consistency

Abstract: In this paper, we consider the following semiparametric regression model under fixed design: y_i=x_i¹β+g(x_i)+e_i. The estimators of β, g(·) and σ²are obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.

Key words: semiparametric , regression , model, least , square , estimation, weight , function, strong consistency

中图分类号:

： O212.7

田萍, 薛留根. 固定设计下一类半参数回归模型估计的强相合性[J]. 数学季刊, 2006, 21(2): 202-209.

TIAN Ping, XUE Liu-gen. Strong Consistency of Estimators of a Semiparametric Regression Model under Fixed Design[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(2): 202-209.

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