Robustness against unexpected dependence in the location model

Robustness of M-estimates of location against unexpected dependence in the data is studied via a min--max asymptotic variance approach. A measure of dependence is defined and used to construct a neighborhood of the classical location model which includes dependent observations. The solution of the min--max problem is a Huber's type M-estimate with psi-function [psi]c. The tuning constant c tends to zero, i.e. [psi]c(x) --> sign(x) (the sample median score function), when the maximum degree of dependence allowed in the neighborhood increases. Thus the median, which is the most bias-robust estimate of location, is also approximately the most variance-robust in the present context.