Abstract
This article gives a simple result for the expression of the Fisher information in order statistics. This result enables us to calculate easily the Fisher information in any set of order statistics whose details have been known to be messy and complicated. We consider here its application in the optimal spacing problem where the exact Fisher information in order statistics has been approximated with the asymptotic information or the reciprocal of the variance of a suitable estimator.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnold, B. C., Balakrishnan, N., and Nagaraja, H. N. (1992),A first course in order statistics, New York: John Wiley.
Balmer, D. W., Boulton, M. and Sack, R. A. (1974), Optimal solution in parameter estimation problems for the Cauchy distribution.Journal of the American Statistical Association 69, 238–242.
Bofinger, E. (1975), Optimal condensation of distributions and optimal spacing of order statistics.Journal of the American Statistical Association 70, 151–154.
Chan, L. K. and Cheng, S. W. (1974), An algorithm for determining the asymptotically best linear estimate of mean from multiply censored logistic data.Journal of the American Statistical Association 69, 1027–1030.
Chan, L. K., Chan, N. N. and Cheng, S. W. (1971), Best linear unbiased estimate of the parameters of the logistic distribution based on selected order statistics.Journal of the American Statistical Association 66, 889–892.
Cheng, S. W. (1975), A unified approach to choosing optimum quantiles for the ABLE's.Journal of the American Statistical Association 70, 155–159.
David, H. A. (1981),Order statistics, New York: John Wiley.
Halperin, M. (1952), Maximum likelihood estimation in truncated samples.Annals of Mathematical Statistics 23, 226–238
Hassanein, K. M. (1969), Estimation of the parameters of the extreme value distribution by use of two or three order statistics.Biometrika 56, 429–436.
Johnson, R. A. and Wichern, D. W. (1992),Applied multivariate statistical analysis. Prentice Hall.
Kubat, P. and Epstein, B. (1980), Estimation of quantiles of locationscale distributions based on two or three order statistics.Technometrics 22, 575–581.
Kulldorff, G. (1973), A note on the optimum spacing of sample quantiles from the six extreme value distributions.Annals of Statistics 1, 562–567.
Murthy, V. K. and Swartz, G. B. (1975), Estimation of Weibull parameters for two order statistics.Journal of the Royal Statistical Society B 37, 96–102.
Ogawa, J. (1998), Optimal spacing of the selected sample quantiles for the joint estimation of the location and scale parameters of a symmetric distribution.Journal of Statistical Planning and Inference 70, 345–360.
Park, S. (1996), Fisher information in order statistics,Journal of the American Statistical Association 91, 385–390.
Saleh, A. K. Md. E., Ali, M. M. and Umbach, D. (1983), Estimating the quantile function of a location-scale family of distributions based on few selected order statistics.Journal of Statistical Planning and Inference 8, 75–86.
Zheng, G. and Gastwirth, J. L. (2000), Where is the Fisher information in an ordered sample?Statistica Sinica 10, 1267–1280.
Author information
Authors and Affiliations
Additional information
This work was supported by Korea Research Foundation Grant(KRF-2000-015-DP0056)
Rights and permissions
About this article
Cite this article
Park, S. On calculating the fisher information in order statistics. Statistical Papers 46, 293–301 (2005). https://doi.org/10.1007/BF02762973
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02762973