Statistics & Probability Letters 77 (2007) 964–972 Fisher information in record values and their concomitants about dependence and correlation parameters Morteza Amini, J. Ahmadi Ã,1 Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran Received 15 December 2005; received in revised form 4 December 2006; accepted 17 January 2007 Available online 9 February 2007 Abstract Let fðX i ; Y i Þ; iX1g be a sequence of bivariate random variables from a continuous distribution with single real valued parameter y. 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 y 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 y whose variance is equal to Crame´r–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 y 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. r 2007 Elsevier B.V. All rights reserved. MSC: 62G30; 62B10; 62F10; 62F12 Keywords: Archimedean copulas; Bivariate normal distribution; Farlie–Gumbel–Morgenstern family; Gumbel–Hougaard model; Relative efficiency 1. Introduction Recently, the problem of finding the efficient estimators based on record values, caused the researchers to take the evaluation of the corresponding Fisher information into concern. In order to find an answer for the question ‘‘How much information contained in record values?’’, Ahmadi and Arghami (2001), Stepanov et al. (2003) and Balakrishnan and Stepanov (2005) have been working on the Fisher information contained in ARTICLE IN PRESS www.elsevier.com/locate/stapro 0167-7152/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.spl.2007.01.003 Ã Corresponding author. Fax: +98 51 18828605. E-mail addresses: mort_amini@gmail.com (M. Amini), ahmadi@math.um.ac.ir (J. Ahmadi). 1 The second author is a member of Statistics Center of Excellence of Ferdowsi University of Mashhad.