NA样本部分线性模型估计的强相合性

周兴才;胡舒合

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (1) : 60-071.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (1) : 60-071. DOI: 10.12341/jssms08917
论文

NA样本部分线性模型估计的强相合性

    周兴才(1), 胡舒合(2)
作者信息 +

Strong Consistency of Estimators in Partial Linear Model Under NA Samples

    ZHOU Xingcai(1), HU Shuhe(2)
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摘要

考虑回归模型: Y(j)(xin,tin)=tinβ+g(xin)+σine(j)(xin),1≤j≤m,1≤i≤n,其中σin2=f(uin),(xin,tin,uin)为固定非随机设计点列, β是未知待估参数,g(⋅)和f(⋅)是未知函数,误差{e(j)(xin)}是均值为零的NA变量.给出基于g(⋅)和f(⋅)一类非参数估计的β的最小二乘估计和加权最小二乘估计, 并在适当条件下得到了它们的强相合性.

Abstract

Consider the heteroscedastic regression model:Y(j)(xin,tin)=tinβ+g(xin)+σine(j)(xin),1≤j≤m,1≤i≤n, where σin2=f(uin), (xin,tin,uin) are fixed design points, β is an unknown parameter, g(⋅) and f(⋅) are unknown functions, and the errors {e(j)(xin)} are mean zero NA random variables. The strong consistency for least-squares estimator and weighted least-squares estimator of β is studied based on the family of nonparametric estimates of g(⋅) and f(⋅).

关键词

部分线性模型 / NA变量 / 最小二乘估计 / 强相合性.

Key words

Partial linear model / NA random variable / least-squares estimator / strong consistency.

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周兴才 , 胡舒合. NA样本部分线性模型估计的强相合性. 系统科学与数学, 2010, 30(1): 60-071. https://doi.org/10.12341/jssms08917
ZHOU Xingcai , HU Shuhe. Strong Consistency of Estimators in Partial Linear Model Under NA Samples. Journal of Systems Science and Mathematical Sciences, 2010, 30(1): 60-071 https://doi.org/10.12341/jssms08917
中图分类号： 62G05   
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