The classical point estimation problem is investigated under alternative loss functions which are quasi-convex and symmetric with respect to some subgroup of the orthogonal group in n. A characterization of better estimators is proved and applied to scale and translation families of estimators....

Two extensions of the univariate Gini index are considered:RD, based on expected distance between two independent vectors from the same distribution with finite mean[mu][set membership, variant]d; andRV, related to the expected volume of the simplex formed fromd+1 independent such vectors. A new...

A general notion of trimmed regions for empirical distributions in d-space is introduced. The regions are called weighted-mean trimmed regions. They are continuous in the data as well as in the trimming parameter. Further, these trimmed regions have many other attractive properties. In...