Research Of M-Estimation In Linear Models And Its Application

This paper studies the theory about robustness of linear models-M-method in linearmodels. Mainly, large samples properties and numerical simulation algorithm are studied when convex functions are taken as loss functions.Firstly, in the case of iid. large samples, the limiting character of S~l are studied and sufficient conditions of weak consistency of M estimators in linear models are discussed. The structure of S-1n is got by the method of projection analysis under its statistical surrounding. It is shown that main diagonal elements of S-1n is descending themselves when n→∞ .which makes the other elements of S-1n descending on the whole at the same time.Secondly , in the case of iid. large samples, the algebraic properties of dn = max1