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Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates. (English) Zbl 1156.62036
Summary: We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-squares 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-squares 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.

MSC:
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62H15 Hypothesis testing in multivariate analysis
62G10 Nonparametric hypothesis testing
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