Estimation of a common parameter for pooled samples from the uniform distributions

  • Masafumi Akahira
  • Kei Takeuchi
Article
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Summary

The problem to estimate a common parameter for the pooled sample from the uniform distributions is discussed in the presence of nuisance parameters. The maximum likelihood estimator (MLE) and others are compared and it is shown that the MLE based on the pooled sample is not (asymptotically) efficient.

Key words and phrases

Maximum likelihood estimator weighted estimator uniform distributions 

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References

  1. [1]
    Akahira, M. (1975). Asymptotic theory for estimation of location in non-regular cases, I: Order of convergence of consistent estimators,Rep. Statist. Appl. Res., JUSE,22, 8–26.MATHMathSciNetGoogle Scholar
  2. [2]
    Akahira, M. (1975). Asymptotic theory for estimation of location in non-regular cases, II: Bounds of asymptotic distributions of consistent estimators,Rep. Statist. Appl. Res., JUSE,22, 99–115.MATHGoogle Scholar
  3. [3]
    Akahira, M. (1976). A remark on asymptotic sufficiency of statistics in non-regular cases,Rep. Univ. Electro-Comm.,27, 125–128.MathSciNetGoogle Scholar
  4. [4]
    Akahira, M. (1982). Asymptotic optimality of estimators in non-regular cases,Ann. Inst. Statist. Math., A,34, 69–82.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Akahira, M. (1982). Asymptotic deficiencies of estimators for pooled samples from the same distribution, Probability Theory and Mathematical Statistics,Lecture Notes in Mathematics,1021, 6–14, Springer, Berlin.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Akahira, M. and Takeuchi, K. (1981). Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency,Lecture Notes in Statistics 7, Springer, New York.MATHGoogle Scholar
  7. [7]
    Akahira, M. and Takeuchi, K. (1982). On asymptotic deficiency of estimators in pooled samples in the presence of nuisance parameters,Statistics and Decisions,1, 17–38, Akademische Verlagsgesellschaft.MATHMathSciNetGoogle Scholar
  8. [8]
    Akai, T. (1982). A combined estimator of a common parameter,Keio Science and Technology Reports,35, 93–104.MATHMathSciNetGoogle Scholar
  9. [9]
    Antoch, J. (1984). Behaviour of estimators of location in non-regular cases: A Monte Carlo study, Asymptotic Statistics 2,the Proceedings of the 3rd Prague Symposium on Asymptotic Statistics, 185–195, North-Holland, Amsterdam.Google Scholar
  10. [10]
    Ibragimov, I. A. and Has'minskii, R. Z. (1981).Statistical Estimation: Asymptotic Theory, Springer, New York.MATHGoogle Scholar
  11. [11]
    Jurečková, J. (1981). Tail-behaviour of location estimators in non-regular cases,Commentationes Mathematicae Universitatis Carolinae,22, 365–375.MathSciNetMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1985

Authors and Affiliations

  • Masafumi Akahira
    • 1
    • 2
  • Kei Takeuchi
    • 1
    • 2
  1. 1.University of Electro-CommunicationsJapan
  2. 2.University of TokyoTokyoJapan

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