Adaptive Efficient Weighted Least Squares With Dependent Observations

Abstract

Work of Eicker [1963], Hinkley [1977] and White [1980] has established straightforward methods for consistently estimating the asymptotic covariance matrix of the ordinary least squares (OLS) estimator for the parameters of the linear regression model despite the possible presence of heteroskedasticity of unknown form. In this sense, such covariance matrix estimators are “robust” to unequal scale of the regression errors. Cragg [1983] proposed parameter estimators that exploit unknown heteroskedasticity to achieve gains in relative efficiency, in the sense that Cragg’s estimators have smaller asymptotic variance than OLS. However, Cragg’s estimators are not guaranteed to have minimum asymptotic variance, so the presence of heteroskedasticity of unknown form can still have adverse consequences for the power of tests based on these estimators.