Fisher information in record values and their concomitants about dependence and correlation parameters

Let {(Xi,Yi),i⩾1} be a sequence of bivariate random variables from a continuous distribution with single real valued parameter θ. In this paper, we investigate the properties of Fisher information about the dependence and correlation parameters in the sequence of the first n records and their concomitants and compare it with the desired information in an i.i.d. sample of size n from a bivariate distribution. Under the assumption that the marginal distribution of X is free of θ the additivity property of the Fisher information is investigated. An explicit expression of Fisher information in record values and their concomitants is given for the Farlie-Gumbel-Morgenstern (FGM) copula family which are parameterized by dependence parameter. It is shown that the Fisher information contained in record values and their comcomitants is more than that of the same number of i.i.d. bivariate observations from FGM family of distributions. The relative efficiency (RE) of that estimator of θ whose variance is equal to Cramér-Rao lower bound, based on record values and their concomitants and i.i.d. observations are studied. Similar results are obtained for bivariate normal in the case that θ is correlation parameter. Finally some numerical results for the corresponding RE for the estimators of Kendall's correlation parameter, tau, are given for one of the most common families of Archimedean Copulas, namely Gumbel-Hougaard model.