Statistical inference for heteroscedastic semi-varying coefficient EV models

Abstract

This paper proposes an estimation procedure for a class of semi-varying coefficient regression models when the covariates of the linear part are subject to measurement errors. Initial estimates for the regression and varying coefficients are first constructed by the profile least-squares procedure without input from heteroscedasticity, a bias-corrected kernel estimate for the variance function then is proposed, which in turn is used to define re-weighted bias-corrected estimates of the regression and varying coefficients. Large sample properties of the proposed estimates are thoroughly investigated. The finite-sample performance of the proposed estimates is assessed by an extensive simulation study and an application to the Boston housing data set. The simulation results show that the re-weighted bias-corrected estimates outperform the initial estimates and the naive estimates.