线性误差协变量下部分线性模型的约束统计推断

doi:10.6040/j.issn.1671-9352.0.2014.139

山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (07): 69-74.doi: 10.6040/j.issn.1671-9352.0.2014.139

线性误差协变量下部分线性模型的约束统计推断

赵培信¹, 周小双²

1. 河池学院数学与统计学院, 广西宜州 546300;
2. 德州学院数学科学学院, 山东德州 253000

收稿日期:2014-04-08 出版日期:2014-07-20 发布日期:2014-09-15
作者简介:赵培信（1981- ），男，博士，教授，主要研究方向为非参数统计. E-mail：zpx81@163.com
基金资助:
国家自然科学基金资助项目（11101119）；广西中青年优秀骨干教师培养工程资助项目

Restricted statistical inference for partially linear models with error-prone covariates

ZHAO Pei-xin¹, ZHOU Xiao-shuang²

1. College of Mathematics and Statistics, Hechi University, Yizhou 546300, Guangxi, China;
2. College of Mathematics Sciences, Dezhou University, Dezhou 253000, Shandong, China

Received:2014-04-08 Online:2014-07-20 Published:2014-09-15

摘要/Abstract

摘要： 考虑含有线性误差协变量部分线性模型的统计推断问题。对模型的参数分量，提出了一个线性约束条件下的最小二乘估计，并且证明该估计量满足渐近正态性。同时基于拉格朗日乘子检验方法对约束条件的合理性进行了检验。证明了所提出的检验统计量在原假设成立时渐近服从标准卡方分布。数据模拟表明所提出的估计方法可以有效地消除测量误差对估计精度的影响，并且所提出的检验方法对备择假设是相当敏感的。

关键词: 拉格朗日乘子检验, 部分线性模型, 线性误差协变量, 约束估计

Abstract: The statistical inference for the partially linear models with error-prone covariates were considered. A restricted least square estimation procedure of parametric components was proposed, and the resulting estimator was shown to be asymptotic normality. Moreover, a Lagrange multiplier testing method was proposed to test the validity of the linear restriction. It was proved that the proposed testing statistic follows an asymptotic standard Chi-square distribution under the null hypothesis. Simulation studies imply that the proposed estimation procedure can attenuate the effect of measurement errors, and the proposed testing method is more powerful.

Key words: error-prone covariates, restricted estimator, partially linear models, Lagrange multiplier test

中图分类号:

O212.7

赵培信, 周小双. 线性误差协变量下部分线性模型的约束统计推断[J]. 山东大学学报（理学版）, 2014, 49(07): 69-74.

ZHAO Pei-xin, ZHOU Xiao-shuang. Restricted statistical inference for partially linear models with error-prone covariates[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 69-74.

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线性误差协变量下部分线性模型的约束统计推断

Restricted statistical inference for partially linear models with error-prone covariates

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