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On the asymptotic Fisher information in order statistics

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Abstract

We extend the result of Efron and Johnstone (1990), who expressed the Fisher information in terms of the hazard function, to express the Fisher information in order statistics as an expectation of the incomplete integral of the hazard function. Then we obtain the the asymptotic Fisher information in terms of the incomplete integral of the hazard function. We also provide an asymptotic information plot, where we can instantly read the proportion of asymptotic information for any given quantile.

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References

  • Bickel PJ (1967) Some contributions to the theory of order statistics. Proc. of Fifth Berkeley Symp. Math. Statist. Prob. 1:575–591

    MathSciNet  Google Scholar 

  • Blom G (1958) Statistical estimates and transformed beta variables. John Wiley, New York

    MATH  Google Scholar 

  • Efron B, Johnstone I (1990) Fisher information in terms of the hazard rate. Annals of Statistics 18:38–62

    Article  MATH  MathSciNet  Google Scholar 

  • Escobar LA and Meeker WQ (2001) The asymptotic equivalence of the Fisher information matrices for Type 1 and Type II censored data from location-scale families. Communications in Statistics. Theory and Methods 30:2211–2225

    Article  MATH  MathSciNet  Google Scholar 

  • Gertsbakh I (1995) On the Fisher information in the type-I censored and quantal response data. Statistics and Probability Letters 23:297–306

    Article  MATH  MathSciNet  Google Scholar 

  • Halperin M (1952) Maximum likelihood estimation in truncated samples. Annals of Mathematical Statistics 23:226–238

    Article  MATH  MathSciNet  Google Scholar 

  • Johnson RA (1974) Asymptotic results for inference procedures based on the r smallest observations. Annals of Statistics 2:1138–1151

    Article  MATH  MathSciNet  Google Scholar 

  • Mehrotra KG, Johnson RA, Bhattacharyya, GK (1979) Exact Fisher information for censored samples and the extended hazard rate functions. Communications in Statistics, Theory and Methods 15:1493–1510

    Article  MathSciNet  Google Scholar 

  • Park S (1996) Fisher information in order statistics. Journal of the American Statistical Association 91:385–390

    Article  MATH  MathSciNet  Google Scholar 

  • Sen PK (1959) On the moments of the sample quantiles. Calcutta Statist. Assoc. Bull. 9:1–20

    MATH  MathSciNet  Google Scholar 

  • Stigler SM (1969) Linear functions of order statistics. Annals of Mathematical Statistics 40:770–788

    Article  MATH  MathSciNet  Google Scholar 

  • Zheng G (2000) A characterization of the factorization of hazard function by the Fisher information under Type II censoring with application to the Weibull family. Statistics and Probability Letters 52:249–253

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Statistics, Yonsei University, Shinchon Dong 134, Seoul, South Korea

    Sangun Park

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  1. Sangun Park
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Correspondence to Sangun Park.

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Park, S. On the asymptotic Fisher information in order statistics. Metrika 57, 71–80 (2003). https://doi.org/10.1007/s001840200200

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  • DOI: https://doi.org/10.1007/s001840200200

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