S-estimation in the nonlinear regression model with long-memory error terms

Abstract

In this paper we consider the asymptotic distribution of S-estimators in the nonlinear regression model with long-memory error terms. S-estimators are robust estimates with a high breakdown point and good asymptotic properties in the iid case. They are constructed for linear regression. In the nonlinear regression model with long-memory errors it turns out, that S-estimators are asymptotically normal with a rate of convergence of n^1-H , 1/2<H<1. But the distribution depends heavily on the unknown parameter vector.