Optimality of the least weighted squares estimator. (English) Zbl 1245.62013

Summary: The present paper deals with the least weighted squares estimator which is a robust estimator and generalizes classical least trimmed squares. We prove \(\sqrt {n}\)-consistency and asymptotic normality for any sequence of roots of normal equations for the location model. The influence function for the general case is calculated. Finally, optimality of this estimator is discussed and formulas for most B-robust and most V-robust weights are derived.


62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
62J05 Linear regression; mixed models
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