It is straightforward that breaking the <em>orthogonalitycondition</em> implies biased and inconsistent estimates by means of the<em> ordinary least squares</em>. If moreover, the data are contaminatedit may significantly worsen the data processing, even if it is performed by <em> instrumental variables</em> or the <em>(scaled) total least squares</em>. That is why the method of <em> instrumental weighted variables</em> 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 <em>neglecting heteroscedasticity</em> may end up in <em>significantly wrongspecification</em> and <em> identification</em> of regression model, justdue to wrong evaluation of <em>significance of the explanatoryvariables</em>. So, if the test of heteroscedasticity (which is in thecase when we use the instrumental weighted variables justrobustified version of the classical White test forheteroscedasticity) rejects the hypothesis of homoscedasticity, we need an <em>estimator of covariance matrix (of the estimators of regression coefficients) resistant to heteroscedasticity</em>. The proposal of such an estimator is the main result of the paper. At the end of paper the <em>numerical study of the proposed estimator </em>(together with results offering comparison of model estimation by means of the ordinary least squares, the least weighted squares andby the instrumental weighted variables) is included.
