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Consistency of the least weighted squares under heteroscedasticity. (English) Zbl 1220.62064
Summary: A robust version of 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 solutions of the corresponding extremal problem and the consistency under heteroscedasticity is proved.

MSC:
62H12 Estimation in multivariate analysis
62G30 Order statistics; empirical distribution functions
62J05 Linear regression; mixed models
62F35 Robustness and adaptive procedures (parametric inference)
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