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

TL;DR

This paper develops estimation and testing procedures for semiparametric varying-coefficient partially linear models with error-prone covariates, using calibration, asymptotic analysis, and bootstrap methods.

Contribution

It introduces a novel profile least-square estimation method for models with unobserved covariates and error calibration, along with improved small-sample tests.

Findings

Estimation procedures are asymptotically consistent and efficient.

Proposed tests effectively identify significant model components.

Bootstrap methods improve test accuracy for small samples.

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.