Robust analogs of the Qn-estimate of scale for the Student distributions

Abstract

Robust computationally fast Huber’s MQ n -estimates of scale are designed to approximate the highly robust and efficient Q n -estimate of scale proposed by Rousseeuw and Croux (1993). The parameters of this approximation are tuned to provide high robustness and efficiency of these M-estimates of scale for the Student distributions—the dependencies between the values of the estimate parameter and distribution shape parameter are written out and tabulated. The comparative study of robust estimates is performed by computation of their asymptotic efficiencies and breakdown points. A special attention is payed to the particular cases of the Gaussian and Cauchy distributions