Abstract: Consider a random sample of size from an absolutely continuous bivariate distribution of . Let denote the th order statistic of the sample values and its concomitant, the -value associated with . In this article we are interested in the asymptotic behavior of some functionals of concomitants. Given two increasing integer sequences and with , let and . We investigate the limiting distributions of , , , and when or for . The statistics and can be viewed as range and midrange, respectively. Our results generalize those obtained in Nagaraja and David (1994). We also use these results to investigate the problem of locating the maximum of a nonparametric regression function as discussed in Chen, Huang and Huang (1996).
Key words and phrases: Concomitants of order statistics, regression model.