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

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  • Amini, Morteza
  • Ahmadi, J.

Abstract

Let {(Xi,Yi),i[greater-or-equal, slanted]1} be a sequence of bivariate random variables from a continuous distribution with single real valued parameter [theta]. 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 [theta] 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 [theta] whose variance is equal to Cramer-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 [theta] 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.

Suggested Citation

  • Amini, Morteza & Ahmadi, J., 2007. "Fisher information in record values and their concomitants about dependence and correlation parameters," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 964-972, June.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:10:p:964-972
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    References listed on IDEAS

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    1. Z. Abo-Eleneen & H. Nagaraja, 2002. "Fisher Information in an Order Statistic and its Concomitant," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 667-680, September.
    2. Balakrishnan, N. & Chan, P. S., 1998. "On the normal record values and associated inference," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 73-80, July.
    3. Glenn Hofmann & N. Balakrishnan, 2004. "Fisher information ink-records," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 383-396, June.
    4. Glenn Hofmann, 2004. "Comparing the Fisher information in record data and random observations," Statistical Papers, Springer, vol. 45(4), pages 517-528, October.
    5. Modarres, Reza & Zheng, Gang, 2004. "Maximum likelihood estimation of dependence parameter using ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 315-323, July.
    6. Stepanov, A. V. & Balakrishnan, N. & Hofmann, Glenn, 2003. "Exact distribution and Fisher information of weak record values," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 69-81, August.
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