不同自变量的变系数模型的估计

冯井艳;张日权;张志强

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (2) : 225-235.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (2) : 225-235. DOI: 10.12341/jssms08936
论文

不同自变量的变系数模型的估计

    冯井艳(1), 张日权(2), 张志强(3)
作者信息 +

Estimation of Varying-Coefficient Regression Models with Different Smoothing Variables

    FENG Jingyan(1), ZHANG Riquan(2), ZHANG Zhiqiang(3)
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摘要

讨论具有不同自变量的变系数模型的函数系数的估计及其大样本性质.使用局部线性方法和积分方法,得到函数系数的积分估计;由于该估计有较大的方差,进一步使用回切法改进这一估计,获得了函数系数的改进估计;同时,研究了改进估计的渐近正态性.最后,用模拟例子说明提出的估计方法是有效的.

Abstract

In the paper, the varying-coefficient regression models with different smoothing variables in different coefficient functions are discussed. First, the integrated estimates of the coefficient functions are given by integrating the sample on the initial value obtained by local linear technique. Then, the improvement estimates of the coefficient functions are proposed by a one-step back-fitting procedure on the integrated estimates. The improvement estimators share the same asymptotic normalities as the local linear estimators for the varying coefficient models with a single smoothing variable in different functions. Finally the simulation example shows that the procedure is effective.

关键词

变系数模型 / 局部线性方法 / 积分方法 / 回切法 / 渐近正态性.

Key words

Varying-coefficient regression models / different smoothing variables / local linear method / integrated estimate / back-fitting procedure / asymptotic normality.

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冯井艳 , 张日权 , 张志强. 不同自变量的变系数模型的估计. 系统科学与数学, 2010, 30(2): 225-235. https://doi.org/10.12341/jssms08936
FENG Jingyan , ZHANG Riquan , ZHANG Zhiqiang. Estimation of Varying-Coefficient Regression Models with Different Smoothing Variables. Journal of Systems Science and Mathematical Sciences, 2010, 30(2): 225-235 https://doi.org/10.12341/jssms08936
中图分类号： 62G20   
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