Further Remarks on Robust Estimation in Dependent Situations

Abstract

Results of an earlier paper giving first order optimal robust $M$-estimators of a location parameter in certain dependent situations are extended to the case where the dependency can be modeled by a symmetric form of a $(2k + 1)$st order moving average scheme. It is also shown that the results can not be extended to finding second order optimal $M$-estimators. That is, no $M$-estimators can be optimal to the second order unless they explicitly adapt themselves to the assumed model for dependency.