Concomitant of ordered multivariate normal distribution with application to parametric inference

Abstract

In statistics, the concept of a concomitant, also called the induced order statistic, arises when one sorts the members of a random sample according to corresponding values of another random sample. Indeed, multivariate order statistics induced by the ordering of linear combinations of the components arises naturally in many instances. As a contribution, we provide a general second-order statistical prediction of concomitant of order statistics for multivariate normal distribution, generalizing earlier works. We exemplify its usefulness in parametric inference via two examples related to deterministic and Bayesian estimation.