Comparison of several estimators for the covariance of the coefficient matrix

Abstract

The standard regression analysis assumes that the variances of the disturbance terms are constant, and the ordinary least squares (OLS) method employs this very crucial assumption to estimate the covariance of the disturbance terms perfectly, but OLS fails to estimate well when the variance of the disturbance terms vary across the observations. A very good method suggested by Eicker and improved by White to estimate the covariance matrix of the disturbance terms in case of heteroskedeisticity was proved to be biased. This paper evaluates the performance of White’s method as well as the OLS method in several different settings of regression. Furthermore, bootstrapping, a new method which very heavily depends on computer simulation is included. Several types of this method are used in several cases of homoskedastic, heteroskedastic, balanced, and unbalanced regressions.