More on Stochastic Comparisons and Dependence among Concomitants of Order Statistics

For a sample of iid observations {(Xi, Yi)} from an absolutely continuous distribution, the multivariate dependence of concomitants Y[]=(Y[1], Y[2], …, Y[n]) and the stochastic order of subsets of Y[] are studied. If (X, Y) is totally positive dependent of order 2, Y[] is multivariate totally positive dependent of order 2. If the conditional hazard rate function of Y given X, hY∣X(y∣x), is decreasing in x for every y, Y[] is multivariate right corner set increasing. And if Y is stochastically increasing in X, the concomitants are increasing in multivariate stochastic order.