Consistent estimation of location region

Asymmetric multivariate probability distributions can be difficult to characterize in terms of their location. The works of Doksum (1975, Scand. J. Statist., 2, 11–22) and Blough (1985, Ann. Inst. Statist. Math., 37, 545–555) provide the construction of a location region for a given distribution. Any point in this closed, convex region will serve as a location parameter. It is the purpose of this paper to obtain a consistent estimator of the location region. Consistency is defined in terms of an appropriate pseudometric.