Bahadur representations of M-estimators and their applications in general linear models.

Consider the linear regression model where are general dependence errors. The Bahadur representations of M-estimators of the parameter are given, by which asymptotically the theory of M-estimation in linear regression models is unified. As applications, the normal distributions and the rates of strong convergence are investigated, while are -dependent, and the martingale difference and -weakly dependent.