The estimator variances resulting from a Least Squares Fit are
normally calculated under the assumption of
the homoskedasticity of the underlying data.
However, empirical data often
exhibits heteroskedastic behavior, meaning the variance is not
constant across a variable or variables. Under
heteroskedastic conditions, White's Robust Variance estimates provide
consistent measures of estimator variance in Least Squares regressions.
Method
White's Robust Variance is computed from the regression results using the following formula:
Normally the Omega matrix is
estimated by a diagonal matrix containing the squares of the variance
of all terms. However, in a heteroskedastic situation, this
variance is not constant amongst all terms. The White estimate
uses the residuals of the Least Squares Fit instead of the common variance. In other words, the Omega
matrix contains the squares of the OLS residuals along the diagonal and
zero elsewhere. The resulting covariance matrix estimate is
consistent when the regressed data exhibits heteroskedasticity.