S-estimation in the linear regression model with long-memory error terms under trend

The asymptotic distribution of S-estimators in the linear regression model with long-memory error terms is obtained under mild regularity conditions to the regressors which are sufficiently weak to cover, for example, polynomial trends and i.i.d. carriers, It turns out that S-estimators are asymptotically normal in the case of deterministic regressors with a variance-covariance structure similar to the structure in the i.i.d. case. Also, the rate of convergence for S-estimators is the same as for the least-squares estimator (LSE) and the best linear unbiased estimator (BLUE).