Journal of Mathematical Sciences

, Volume 81, Issue 1, pp 2421–2423 | Cite as

On the location parameter confidence intervals based on a random size sample from a partially known population

  • L. B. Klebanov
  • J. A. Melamed


The problem of constructing confidence intervals of a fixed length for the location parameter based on a random size sample is considered. It is proposed to use the confidence interval
$$\theta _p^* - u\sqrt p /\sigma< \theta< \theta _p^* + u\sqrt p /\sigma $$
, whereθ p * is an adaptive estimator,σ2 is the Fisher information, and p−1 is the mean of the sample size. Nonparametric bounds are given for the limit as p → 0 confidence probability. Bibliography: 5 titles.


Confidence Interval Location Parameter Fisher Information Fixed Length Confidence Probability 
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Literature Cited

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    I. A. Ibragimov and R. Z. Khas'minskii,Asymptotic Theory of Estimation [in Russian], Nauka, Moscow (1979).Google Scholar
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    R. Beran, “An efficient and robust adaptive estimator of location,”Ann. Statist.,6, 292–313 (1978).MATHMathSciNetGoogle Scholar
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    R. L. Dobrushin, “A lemma on the limit of composite random functions,”Usp. Mat. Nauk,10, No. 2, 157–159 (1955).MATHGoogle Scholar
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    J. A. Melamed, “Asymptotic behavior of some statistical estimators in the scheme of estimators of parameters based on a random size sample,”Soobshch. Akad. nauk Gruzii,135, No. 2, 281–284 (1989).MATHMathSciNetGoogle Scholar
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    R. E. Barlow and F. Proshan,Mathematical Theory of Reliability, John Wiley (1964).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • L. B. Klebanov
  • J. A. Melamed

There are no affiliations available

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