Noise benefits to robust M-estimation of location in dependent observations

In the presence of weakly dependent noise, we analyze the asymptotic efficiency of robust maximum likelihood type estimators (M-estimators) for location estimation. We observe the noise-enhanced asymptotic efficiency effect by tuning the background noise level for a single M-estimator. We also theoretically derive the asymptotic efficiency of a parallel array of M-estimators, and illustrate the possibility of the noise enhancement of the asymptotic efficiency by injecting extra additive noise components. These obtained results enrich the research of noise benefits for the robust estimation of location from the dependent observations.