Publication detail

Víšek, J. Á. : Heteroscedasticity resistant robust covariance matrix estimator

Author(s): prof. RNDr. Jan Ámos Víšek CSc.,
Type: Articles in refereed journals
Year: 2010
Number: 17
ISSN / ISBN: ISSN 1212-074x
Published in: Bulletin of the Czech Econometric Society 17(27), 33 - 49.
Publishing place: Prague
Keywords: Robustness, covariance estimator, heteroscedasticity
JEL codes: C13, C19
Suggested Citation:
Grants: 402/09/0557 Robustifikace vybraných ekonometrických metod, hl. řešitel: Prof. RNDr. Jan Ámos Víšek CSc.
Abstract: It is straightforward that breaking the {\it orthogonality
condition} implies biased and inconsistent estimates by means of the
{\it ordinary least squares}. If moreover, the data are contaminated
it may significantly worsen the data processing, even if it is
performed by {\it instrumental variables} or the {\it (scaled) total
least squares}. That is why the method of {\it instrumental
weighted variables} based of weighting down order statistics of
squared residuals (rather than directly squared residuals) was
proposed. The main underlying idea of this method is recalled and
discussed. Then it is also recalled that {\it neglecting
heteroscedasticity} may end up in {\it significantly wrong
specification} and {\it identification} of regression model, just
due to wrong evaluation of {\it significance of the explanatory
variables}. So, if the test of heteroscedasticity (which is in the
case when we use the instrumental weighted variables just
robustified version of the classical White test for
heteroscedasticity) rejects the hypothesis of homoscedasticity, we
need an {\it estimator of covariance matrix (of the estimators of
regression coefficients) resistant to heteroscedasticity}. The
proposal of such an estimator is the main result of the paper. At
the end of paper the {\it numerical study of the proposed estimator}
(together with results offering comparison of model estimation by
means of the ordinary least squares, the least weighted squares and
by the instrumental weighted variables) is included.

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