Huber-Sense Robust M-Estimation of a Scale Parameter, with Application to the Exponential Distribution.

Abstract Huber's (1964) classical theory of robust M-estimation of a location parameter is also applicable to nonnegative data X having scale parameter θ, since Y = log X has location parameter log θ. In the present article, Huber's location parameter results are reformulated in the scale parameter context and then applied to the problem of robust estimation of the parameter of the exponential distribution. The robust M-estimator is obtained here as the solution of a minimax problem, and it turns out to be a type of Winsorized mean.