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

Consider the linear regression model yi = xiTβ + ei,  i = 1, 2, …, n,  where ei = g(…, εi-1, εi) are general dependence errors. The Bahadur representations of M-estimators of the parameter β 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 {εi, i ∈ Z} are m-dependent, and the martingale difference and (ε, ψ) -weakly dependent.