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. |
