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
Article
  • 18 Downloads

Abstract

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.

Keywords

Confidence Interval Location Parameter Fisher Information Fixed Length Confidence Probability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    I. A. Ibragimov and R. Z. Khas'minskii,Asymptotic Theory of Estimation [in Russian], Nauka, Moscow (1979).Google Scholar
  2. 2.
    R. Beran, “An efficient and robust adaptive estimator of location,”Ann. Statist.,6, 292–313 (1978).MATHMathSciNetGoogle Scholar
  3. 3.
    R. L. Dobrushin, “A lemma on the limit of composite random functions,”Usp. Mat. Nauk,10, No. 2, 157–159 (1955).MATHGoogle Scholar
  4. 4.
    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
  5. 5.
    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

Personalised recommendations