serial: Statistics vol.45, 5 (2011), p. 497-508
project(s): GA402/09/0557, GA UK
keywords: Robustness, Convergence, Empirical distribution, Heteroscedasticity
Neglecting heteroscedasticity of error terms may imply a wrong identification of regression. Employment of (heteroscedasticity resistent) White’s estimator of covariance matrix of estimates of regression coefficients may lead to the correct decision about significance of individual explanatory variables under heteroscedasticity. However, 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 available 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.