Abstract
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 contaminated it may worsen the data processing, even if it is performed by instrumental variables or the total least squares.
That is why the method of instrumental weighted variables based of weighting down order statistics of squared residuals was proposed. The main underlying idea of this method is recalled and discussed.
So, if the test of heteroscedasticity rejects the hypothesis of homoscedasticity, we need an estimator of covariance matrix 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 is included.