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Heteroscedasticity Resistant Robust Covariance Matrix Estimator


  • Jan Víšek



It is straightforward that breaking the orthogonality condition implies biased and inconsistent estimates by means of the ordinary least squares . If moreover, the data are contaminatedit may significantly worsen the data processing, even if it is performed by instrumental variables or the (scaled) total least squares . That is why the method of 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 neglecting heteroscedasticity may end up in significantly wrong specification and identification of regression model, just due to wrong evaluation of 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 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 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.

Suggested Citation

  • Jan Víšek, 2010. "Heteroscedasticity Resistant Robust Covariance Matrix Estimator," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 17(27).
  • Handle: RePEc:czx:journl:v:17:y:2010:i:27:id:176

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    Robustification of classical instrumental variables; estimating the;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other


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