Corrected Maximum Likelihood Estimators in Linear Heteroskedastic Regression Models

Abstract

The linear heteroskedastic regression model, for which the variance of the response is given by a suitable function of a set of linear exogenous variables, is very useful in econometric applications. We derive a simple matrix formula for the n^−1 biases of the maximum likelihood estimators of the parameters in the variance of the response, where n is the sample size. These biases are easily obtained as a vector of regression coefficients in a simple weighted least squares regression. We use simulation to compare the uncorrected estimators with the bias-corrected ones to conclude the superiority of the corrected estimators over the uncorrected ones with regard to the normal approximation. The practical use of such biases is illustrated in two applications to real data sets.