• 论文 •

### 线性误差协变量下部分线性模型的约束统计推断

1. 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. 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

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.

• O212.7
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