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....

In multivariate decisions under risk, assessing the complete utility function can be a major obstacle. Decision rules are investigated which characterize uniformly better alternatives with respect to a whole class of utility functions. In this paper independence assumptions are imposed on the...

The Gini index and the Gini mean difference of a univariate distribution are extended to measure the disparity of a general $d$- variate distribution. We propose and investigate two approaches, one based on the distance of the distribution from itself, the other on the volume of a convex set in...

The paper introduces an approach to the ordering of dependence which is based on central regions. A d-variate probability distribution is described by a nested family of sets, called central regions. Those regions are affine equivariant, compact and starshaped and concentrate about a properly...