部分线性变系数模型的Profile Lagrange乘子检验

魏传华;吴喜之

系统科学与数学 ›› 2008, Vol. 28 ›› Issue (4) : 416-424.

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PDF(397 KB)
系统科学与数学 ›› 2008, Vol. 28 ›› Issue (4) : 416-424. DOI: 10.12341/jssms10093
论文

部分线性变系数模型的Profile Lagrange乘子检验

    魏传华(1),吴喜之(2)
作者信息 +

Profile Lagrange Multiplier Test for Partially Linear Varying-Coefficient Regression Models

    WEI Chuanhua(1),WU Xizhi(2)
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文章历史 +

摘要

对于部分线性变系数模型附有约束条件时的估计与检验问题,基于Profile最小二乘方法给出了参数部分以及非参数部分的约束估计并研究了它们的渐近性质, 并针对约束条件构造了Profile Lagrange乘子检验统计量, 证明了该统计量在原假设下的渐近分布为χ2分布,从而将Lagrange乘子检验方法推广到了半参数模型上.

Abstract

The estimation and testing of partially linear varying-coefficient models under additional linear restriction on parametric component are considered.
The constrained estimator for parametric and nonparametric components is established based on Profile least-squares approach, and its asymptotic property is given. For the testing problem, a Profile Lagrange multiplier test statistic is established on the basis of the constrained Profile least-squares estimation.
It is proven that the Profile Lagrange multiplier test statistic is
symptotically distribution-free and followingχ2distribution under the null hypothesis. Finally, the Lagrange multiplier test is successfully applied to semi-parametric models.

关键词

部分线性变系数模型 / 约束估计 / Profile Lagrange乘子检验 / Profile最小二乘估计.

Key words

Partially linear varying-coefficient model / constrained estimators / Profile Lagrange multiplier test / Profile least-squares estimation.

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魏传华 , 吴喜之. 部分线性变系数模型的Profile Lagrange乘子检验. 系统科学与数学, 2008, 28(4): 416-424. https://doi.org/10.12341/jssms10093
WEI Chuanhua , WU Xizhi. Profile Lagrange Multiplier Test for Partially Linear Varying-Coefficient Regression Models. Journal of Systems Science and Mathematical Sciences, 2008, 28(4): 416-424 https://doi.org/10.12341/jssms10093
中图分类号: 62J02    62G05    62G10   
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