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Keywords:
robustness; weighting the order statistics of the squared residuals; consistency of the least weighted squares under heteroscedasticity
robustness; weighting the order statistics of the squared residuals; consistency of the least weighted squares under heteroscedasticity
Summary:
A robust version of the Ordinary Least Squares accommodating the idea of weighting the order statistics of the squared residuals (rather than directly the squares of residuals) is recalled and its properties are studied. The existence of solution of the corresponding extremal problem and the consistency under heteroscedasticity is proved.
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