Consistency and asymptotic normality of profilekernel and backfitting estimators in semiparametric reproductive dispersion nonlinear models  

作　　者：TANG NianSheng CHEN XueDong WANG XueRen 

机构地区：[1]Department of Statistics,Yunnan University,Kunming 650091,China [2]Faculty of Science,Huzhou Normal College,Huzhou 313000,China

出　　处：《Science China Mathematics》2009年第4期757-770,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10561008, 10761011);Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. Y200805073);PhD Special Scientific Research Foundation of Chinese University (Grant No. 20060673002);Program for New Century Excellent Talents in University (Grant No. NCET-07-0737)

摘　　要：Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.

关 键 词：asymptotic normality backfitting method consistency profile-kernel method semiparametric reproductive dispersion nonlinear models 62G05 62G08 62G20 

分 类 号：O212[理学—概率论与数理统计]