Multivariate order statistics via multivariate concomitants

Let X¯1,…,X¯n denote a set of nn independent identically distributed kk-dimensional absolutely continuous random variables. A general class of complete orderings of such random vectors is supplied by viewing them as concomitants of an auxiliary random variable. The resulting definitions of multivariate order statistics subsume and extend orderings that have been previously proposed such as norm ordering and NN-conditional ordering. Analogous concepts of multivariate record values and multivariate generalized order statistics are also described.