Improving the estimation of the offset parameter of heavy-tailed distributions through the injection of noise

Y. Pan, F. Duan, F. Chapeau-Blondeau and D. Abbott, Noise Enhancement in Robust Estimation of Location, IEEE Transactions on Signal Processing, vol. 66, no. 8, pp. 1953-1966, DOI: 10.1109/TSP.2018.2802463.

In this paper, we investigate the noise benefits to maximum likelihood type estimators (M-estimator) for the robust estimation of a location parameter. Two distinct noise benefits are shown to be accessible under these conditions. With symmetric heavy-tailed noise distributions, the asymptotic efficiency of the estimation can be enhanced by injecting extra noise into the M-estimators. With an asymmetric contaminated noise model having a convex cumulative distribution function, we demonstrate that addition of noise can reduce the maximum bias of the median estimator. These findings extend the analysis of stochastic resonance effects for noise-enhanced signal and information processing.

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