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部分线性模型中估计的渐近正态性
引用本文:高集体,陈希孺,赵林城. 部分线性模型中估计的渐近正态性[J]. 数学学报, 1994, 37(2): 256-268. DOI: cnki:ISSN:05831431.0.1994-02-014
作者姓名:高集体  陈希孺  赵林城
作者单位:中国科学技术大学数学系
摘    要:考虑回归模型其中是未知函数,(x_i,t_i,u_i)是固定非随机设计点列,β是待估参数,e_i是随机误差。基于g(·)及f(·)的一类非参数估计(包括常见的核估计和近邻估计),我们构造了β的加权最小二乘估计,并证得了最小二乘估计和加权最小二乘估计的渐近正态性。

关 键 词:部分线性模型,非参数估计,最小二乘估计,加权最小二乘估计,渐近正态性
收稿时间:1992-01-20
修稿时间:1993-04-14

Asymptotic Normality of a Class of Estimators in Partial Linear Models
Goa Jiti, Chen Xiru, Zhao Lincheng. Asymptotic Normality of a Class of Estimators in Partial Linear Models[J]. Acta Mathematica Sinica, 1994, 37(2): 256-268. DOI: cnki:ISSN:05831431.0.1994-02-014
Authors:Goa Jiti   Chen Xiru   Zhao Lincheng
Affiliation:Goa Jiti; Chen Xiru; Zhao Lincheng(Depedment of Mathematics, Univeroity of Science & Technology of china, Hefei,China)
Abstract:Consider the heteroscedastic regression,model y_i=x_iβ+g(t_i)+σ_ie_i forand i=1,2,…,n. Here the design points (x_i,t_i,u_i)are known and nonrandom,g and f areunknown functions, and e_i is an unobserued disturbahce. The family of nonparametric estimatesand including all known estimates is proposed,also proposed is a class of new nearestneighbor estimates of g and f.The least squares estimator β_n and the weighted least squaresestimator are obtained. Some asymptotically efficient estimates are also obtained.
Keywords:partial linear model.asymptotic normality  nonparametric estimation  least-squaresestimate  weighted least-squares estimate  
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