Robust feasible generalized least squares: A remedial measures of heteroscedasticity

The assumption of equal error variances (homoscedasticity) is one of the important assumptions for Least Squares (LS) method in linear regression. However, in man y practical situations equal error variances are not exist and the problem of heteroscedasticity occurs. As a consequence, although the LS method gives unbiased estimate of parameters but it gives biased estimates of the standard errors of the parameters. To overcome this problem of LS method, the Feasible Generalized Least Squares (FGLS) estimator is often suggested in the literature. The FLGS gives unbiased estimate of the parameters and also their standard errors. Nevertheless, there is an evidence that OLS and FLGS estimators suffer a huge set back in the presence of a few atypical observations that we often call outliers. When both outliers and heteroscedasticity exist, the FLGS gives biased estimates and biased standard errors of the parameters. In this article, we proposed to use the Robust Feasible Generalized Least Squares (RFGLS) which his modification of FLGS by incorporating the robust LTS estimator. Numerical results show that the RFLGS offers substantial improvements over the existing FLGS.

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