The Least Weighted Squares Ii. Consistency And Asymptotic Normality

The consistency and the asymptotic normality of the least weighted squares is proved and its asymptotic representation derived. Although the proof includes rather large amount of technicalities, it is not difficult to follow. The technique as follows from the analogy with the least trimmed squares will allow to study also the sensitivity of estimator to the influential points. The results and the properties of the estimator are discussed in the Conclusions at the end of paper.