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研究论文
固定设计点的半参数回归模型的M估计的渐进分布(英文)
Asymptotic Distributions of M-estimators of the Parametric Components of Partly Linear Models with Fixed Carriers

施沛德,滕新东
Shi Peide Teng Xingdong

北京大学概率统计系!中国,北京,100871,北京大学概率统计系!中国,北京,100871
(Dept of Prohabilitg and Statistics, Peking Univ., Beijing, 100871, P. R. China

收稿日期: 1999-10-25
出版日期: 1999-10-25

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摘要 讨论了固定设计点的半参数回归模型的大样本性质,得到了模型的M估计的渐进分布,并建立了关于参数的检验.数值模拟结果表明,本文提出的方法具有较好的稳健性.
关键词 部分线性模型逐段多项式M估计最优收敛率    
Abstract:This paper deals with the problerns of M-estimators for the partly linear model where un are random errors, the (Ti, Xi)'s are known fixed carriers, Xi∈Rd, and Ti ∈ [0, 1], Yi is real-valued, i = 1, 2,''' ,n, β is a d-vector of parameters, and g0(.) is an unknown function. The proposed estimators of β and g0(t) in thi8 paper are β and gn(t)=(t)α respectively, where a and βminimize (.) is a vecor of the basis functions of a piecewise polynomial space and (.) is a function chosen suitably We consider testing the hypothesi8 H0: A"β0 =β. Under some regularity conditions it is shown that β is asytotically normal and the test statistic converges in distribution to a chi square distribution of degree of freedom d0, where ds is the dimension of β. The large-sample tests of linear hypotheses on β show satisfactory performance in our simulated example.
Key words piecewise polynomial    M-estimator    optimal rate of convergence
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