Strong consistency of M-estimates in linear models

This article studies the strong consistency of M-estimates in linear regression models directly from the minimization problem 75, where X1. X2, ... can be random observations of a p-dimensional random vector X, or that they are simply known nonrandom p-vectors. It is shown that the solution ([alpha]n, [beta]'n) of this minimization problem converges with probability one to the true parameter ([alpha]0,[beta]'0) under very general conditions on the function [varrho] and the sequence {(X'i, Yi)}.