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

• 成果类型: Article
• 署名作者: Zhou, Yong; Liang, Hua
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Shanghai University of Finance & Economics; University of Rochester
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS561
• 发表日期: 2009
• 页码: 427-458
• 关键词: estimators

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.