The asymptotic theory of concomitants of order statistics

Abstract

In a random sample of n pairs ( X r , Y r ), r = 1, 2, …, n , drawn from a bivariate normal distribution, let X r : n be the rth order statistic among the X r and let Y [ r : n ] be the Y- variate paired with X r : n . The Y [r:n] , which we call concomitants of the order statistics, arise most naturally in selection procedures based on the X r : n . It is shown that asymptotically the k quantities k fixed, are independent, identically distributed variates. In addition, putting R t , n for the number of integers j for which , the asymptotic distribution and all moments of n – 1 R t, n are determined for t such that t / n → λ with 0 < λ < 1.