Abstract: Consider a random sample of sizefrom 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.