Optimality of the least weighted squares estimator

The present paper deals with least weighted squares estimator which is a robust estimator and generalizes the classical least trimmed squares. We will prove root n-consistency and asymptotic normality for any sequence of roots of normal equation for location model. The influence function for the general case is calculated. Finally optimality of this estimator is discussed and a formula for the most B-robust and most V-robust weights is derived.