Estimation and inference for varying-coefficient regression models with error-prone covariates

Abstract

This paper studies the estimation and inference for a class of varying-coefficient regression models with error-prone covariates. The authors focus on the situation where the covariates are unobserved, there are no repeated measurements, and the covariance matrix of the measurement errors is unknown, but some auxiliary information is available. The authors propose an instrumental variable type local polynomial estimator for the unknown varying-coefficient functions, and show that the estimator achieves the optimal nonparametric convergence rate, is asymptotically normal, and avoids using undersmoothing to allow the bandwidths to be selected using data-driven methods. A simulation is carried out to study the finite sample performance of the proposed estimator, and a real date set is analyzed to illustrate the usefulness of the developed methodology.