Strong unimodality and scale mixtures (Q1060505)

It is known that the asymptotically optimal L-estimator has non-negative weights if and only if the underlying density is strongly unimodal. Since the Tukey model is often used to model data containing gross errors, it is of interest to know when such densities are strongly unimodal. This paper examines the question more generally for a large class of scale mixtures. A simple necessary and sufficient condition is given in the case of the Tukey model.