Minimum distance estimation in an additive effects outliers model

In the additive effects outliers (A.O.) model considered here one observes Yj,n=Xj+υj,n,0≤j≤n, where {Xj} is the first order autoregressive [AR(1)] process with the autoregressive parameter |ρ|<1. The A.O.'s {υj,n,0≤j≤n} are i.i.d. with distribution function (d.f.) (1−γn)I[x≥0]+γnLn(x),x∈R,0≤γn≤1, where the d.f.'s {Ln,n≥0} are not necessarily known. This paper discusses the existence, the asymptotic normality and biases of the class of minimum distance estimators of ρ, defined by Koul, under the A.O. model. Their influence functions are computed and are shown to be directly proportional to the asymptotic biases. Thus, this class of estimators of ρ is shown to be robust against A.O. model.