The Least Weighted Squares I. The Asymptotic Linearity Of Normal Equations

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 assumptions employed in paper as well as the properties as the scale- and regression-equivariance of the estimators are discussed. Since the paper is mostly technical, please pay attention to the Conclusions (in Part II), mainly.