Distribution of order statistics from selected subsets of concomitants

For a random sample of size n from an absolutely continuous bivariate population (X, Y), let Xi:n be the i th X-order statistic and Y[i:n] be its concomitant. We study the joint distribution of (Vs:m, Wt:n−m), where Vs:m is the s th order statistic of the upper subset {Y[i:n], i=n−m+1,…,n}, and Wt:n−m is the t th order statistic of the lower subset {Y[j:n], j=1,…,n−m} of concomitants. When m=⌈np0⌉, s=⌈mp1⌉, and t=⌈(n−m)p2⌉, 0