Abstract
Let (X, Y) have an absolutely continuous distribution with parameter θ. We suggest regularity conditions on the parent distribution that permit the definition of Fisher information (FI) about θ 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 θ, we investigate the properties of this FI, and obtain the asymptotic relative efficiency of the maximum likelihood estimator of θ for Type II censored bivariate samples. Assuming (X, Y) is Gumbel bivariate exponential of second type, and θ 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.
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Abo-Eleneen, Z.A., Nagaraja, H.N. Fisher Information in an Order Statistic and its Concomitant. Annals of the Institute of Statistical Mathematics 54, 667–680 (2002). https://doi.org/10.1023/A:1022479514859
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DOI: https://doi.org/10.1023/A:1022479514859