Skip to main content
SpringerLink
Log in

Bayes sequential estimation for a particular exponential family of distributions under LINEX loss

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

The problem of sequentially estimating an unknown distribution parameter of a particular exponential family of distributions is considered under LINEX loss function for estimation error and a cost c > 0 for each of an i.i.d. sequence of potential observations X 1, X 2, . . . A Bayesian approach is adopted and conjugate prior distributions are assumed. Asymptotically pointwise optimal and asymptotically optimal procedures are derived.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arrow KJ, Blackwell D, Girshick MA (1949) Bayes and minimax solutions of sequential decision problems. Econometrica 17: 213–244

    Article  MathSciNet  Google Scholar 

  • Barlow RE, Proschan F (1988) Life distributions models and incomplete data. In: Krishnaiah PR, Rao CR (eds) Handbook of statistics. Elsevier Science Publishiers BV, Amsterdam, pp 225–249

    Google Scholar 

  • Bickel PJ, Yahav JA (1967) Asymptotically pointwise optimal procedures in sequential analysis. Proc Fifth Berkeley Symp Math Stat Probab 1: 401–413

    MathSciNet  Google Scholar 

  • Bickel PJ, Yahav JA (1968) Asymptotically optimal Bayes and minimax procedures in sequential estimation. Ann Math Stat 39: 442–456

    Article  MathSciNet  MATH  Google Scholar 

  • Bickel PJ, Yahav JA (1969) On an A.P.O. rule in sequential estimation with quadratic loss. Ann Math Stat 40: 417–426

    Article  MathSciNet  MATH  Google Scholar 

  • Bickel PJ, Yahav JA (1969) Some contributions to the asymptotic theory of Bayes solutions. Z Wahrscheinlichkeitsheorie und Verw Gebiete 11: 257–276

    Article  MathSciNet  MATH  Google Scholar 

  • Jozani JM, Nematollahi N, Shafie K (2002) An admissible minimax estimator of a bounded scale parameter in a subclass of the exponential family under scale-invariant squared-error loss. Stat Probab Lett 60: 437–444

    Article  MathSciNet  MATH  Google Scholar 

  • Kiefer J, Sacks J (1963) Asymptotically optimal sequential inference and design. Ann Math Stat 34: 705–750

    Article  MathSciNet  MATH  Google Scholar 

  • López-Blázquez F (1998) A note on UMVUE estimation in the transformed chi-square family. Commun Stat Theory Methods 27: 2065–2073

    Article  MATH  Google Scholar 

  • López-Blázquez F, Barranco-Chammoro I, Moreno-Rebollo JL (1997) UMVUE estimation for certain family of exponential distributions. Commun Stat Theory Methods 26: 469–482

    Article  MATH  Google Scholar 

  • Rahman HS, Gupta RP (1993) Family of transformed chi-square distributions. Commun Stat Theory Methods 2: 135–146

    MathSciNet  Google Scholar 

  • Rehaïlia MEH (1984) Asymptotic sequential analysis in the A.P.O. rule performance. Seq Anal 3: 155–174

    Article  MATH  Google Scholar 

  • Takada Y (2001) Bayes sequential estimation of Poisson mean under LINEX loss function. Seq Anal 20: 55–64

    Article  MathSciNet  MATH  Google Scholar 

  • Varian HR (1975) A Bayesian approach to real estate assessment. In: Fienberg SE, Zellner A (eds) Studies in Bayesian econometrics and statistics in honour of L. J. Savage. North-Holland Publishing Company, Amsterdam, pp 195–208

    Google Scholar 

  • Wald A (1950) Asymptotic minimax solutions of sequential point estimation problems. In: Proc Second Berkeley Symp Math Statist Prob Berkeley and Los Angeles, University of California Press, pp 1–11

  • Woodroofe M (1981) A.P.O. rules are asymptotically non-deficient for estimation with squared error loss. Z Wahrscheinlichkeitsheorie und Verw Gebiete 58: 331–341

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wroclaw, Poland

    Alicja Jokiel-Rokita

Authors
  1. Alicja Jokiel-Rokita
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alicja Jokiel-Rokita.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jokiel-Rokita, A. Bayes sequential estimation for a particular exponential family of distributions under LINEX loss. Metrika 74, 211–219 (2011). https://doi.org/10.1007/s00184-010-0298-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-010-0298-4

Keywords

Mathematics Subject Classification (2000)

Search

Navigation