On multivariate order statistics: Asymptotic theory and computing moments

In this paper, the exact explicit expression for the distribution function of the multivariate order statistics is derived. The advantage of this expression is its facility when one decides to pass to the limit as the sample size increases. The exact limit forms as well as the conditions by which this limit splits into the product of the limit marginals are obtained. In addition, an analytic bootstrap-type method for estimating the product moments (of any order) of multivariate order statistics is exhibited.