Víšek, J. Á.: Empirical distribution function under heteroscedasticity
| Autor: | prof. RNDr. Jan Ámos Víšek CSc., |
|---|---|
| Typ: | Články v impaktovaných časopisech |
| Rok: | 2011 |
| Číslo: | 45 |
| ISSN / ISBN: | 1029-4910 |
| Publikováno v: | Statistics 45, 497-508. |
| Místo vydání: | Taylor & Francis |
| Klíčová slova: | Regression, asymptotics of Kolmogorov-Smirnov statistics under heteroscedasticity, robustified White's estimate of covariance matrix |
| JEL kódy: | |
| Citace: | |
| Abstrakt: | Neglecting heteroscedasticity of error terms may imply a wrong identification of regression model - see Appendix. 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. 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. |
