AISM 54, 667-680
© 2002 ISM
(Received July 14, 2000; revised February 9, 2001)
Abstract. Let $(X,Y)$ have an absolutely continuous distribution with parameter $\theta$. We suggest regularity conditions on the parent distribution that permit the definition of Fisher information (FI) about $\theta$ in an $X$-order statistic and its $Y$-concomitant that are obtained from a random sample from $(X,Y)$. We describe some general properties of the FI in such individual pairs. For the Farlie-Gumbel-Morgenstern parent with dependence parameter $\theta$, we investigate the properties of this FI, and obtain the asymptotic relative efficiency of the maximum likelihood estimator of $\theta$ for Type II censored bivariate samples. Assuming $(X,Y)$ is Gumbel bivariate exponential of second type, and $\theta$ is the mean of $Y$, we evaluate the FI in the $Y$-concomitant of an $X$-order statistic and compare it with the FI in a single $Y$-order statistic.
Key words and phrases: Concomitants of order statistics, Fisher information, Farlie-Gumbel-Morgenstern family, Gumbel Type II bivariate exponential distribution, Type II censoring, maximum likelihood estimator.