The Annals of Statistics

Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates

Yong Zhou and Hua Liang

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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.

Article information

Ann. Statist., Volume 37, Number 1 (2009), 427-458.

First available in Project Euclid: 16 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties 62H15: Hypothesis testing

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


Zhou, Yong; Liang, Hua. Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates. Ann. Statist. 37 (2009), no. 1, 427--458. doi:10.1214/07-AOS561.

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