Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates
The Annals of Statistics · 2009 · Volume 37 · Issue 1
Abstract
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.
Keywords
62G08, 62G10, 62G20, 62H15, Ancillary variables, de-noise linear model, errors-in-variable, profile least-square-based estimator, rational expection model, validation data, wild bootstrap
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