Truncated Estimator of Asymptotic Covariance Matrix in Partially Linear Models with Heteroscedastic Errors

Abstract

A partially linear regression model with heteroscedastic and/or serially correlated errors is studied here. It is well known that in order to apply the semiparametric least squares estimation (SLSE) to make statistical inference a consistent estimator of the asymptotic covariance matrix is needed. The traditional residual-based estimator of the asymptotic covariance matrix is not consistent when the errors are heteroscedastic and/or serially correlated. In this paper we propose a new estimator by truncating, which is an extension of the procedure in White [32] . This estimator is shown to be consistent when the truncating parameter converges to infinity with some rate.