STATISTICAL INFERENCE FOR SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS WITH ERROR-PRONE LINEAR COVARIATES

被引：111

作者：

Zhou, Yong ^{[1
,2
]}

Liang, Hua ^{[3
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China

[2] Shanghai Univ Finance & Econ, Dept Stat, Shanghai 200433, Peoples R China

[3] Univ Rochester, Dept Biostat & Computat Biol, Rochester, NY 14642 USA

来源：

ANNALS OF STATISTICS | 2009年 / 37卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Ancillary variables; de-noise linear model; errors-in-variable; profile least-square-based estimator; rational expection model; validation data; wild bootstrap; ESTIMATORS;

D O I：

10.1214/07-AOS561

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square based estimation procedures are developed for parametric and nonparametric components after we calibrate the error-prone covariates. Asymptotic properties of the proposed estimators are established. We also propose the profile least-square based ratio test and Wald test to identify significant parametric and nonparametric components. To improve accuracy of the proposed tests for small or moderate sample sizes, a wild bootstrap version is also proposed to calculate the critical values. Intensive simulation experiments are conducted to illustrate the proposed approaches.

引用

页码：427 / 458

页数：32

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