Abstract
White's estimator of covariance matrix was established for LS-regression analysis (in the case when error terms are normally distributed, LS- and ML-analysis coincide and hence then White's estimate of covariance matrix is vailable for ML-regression analysis, too). To establish White's-type estimate for another estimator of regression coefficients requires Bahadur representation of the estimator in question, under heteroscedasticity of error terms.
The derivation of Bahadur representation for other (robust) estimators requires some tools. As the key one proved to be a tight approximation of the empirical distribution function of residuals by the theoretical distribution function of the error terms of the regression model.
We need the approximation to be uniform in the argument of distribution function as well as in regression coefficients. The present paper offers this approximation for the situation when the error terms are heteroscedastic.