Publication detail

Víšek, J. Á.: Empirical distribution function under heteroscedasticity

Author(s): prof. RNDr. Jan Ámos Víšek CSc.,
Type: Articles in journals with impact factor
Year: 2011
Number: 45
ISSN / ISBN: 1029-4910
Published in: Statistics 45, 497-508.
Publishing place: Taylor & Francis
Keywords: Regression, asymptotics of Kolmogorov-Smirnov statistics under heteroscedasticity, robustified White's estimate of covariance matrix
JEL codes:
Suggested Citation:
Abstract: 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.

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