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

Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (2): 202-209.

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)；

Abstract

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

CLC Number:

： O212.7

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

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