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Asymptotically pointwise optimal allocation rules in Bayes sequential estimation

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  • Hwang, Leng-Cheng
  • Karunamuni, Rohana J.

Abstract

In this paper, the concept of asymptotic pointwise optimality in a single sequence of random variables provided by Bickel and Yahav [Bickel, P.J., Yahav, J.A., 1967. Asymptotically pointwise optimal procedures in sequential analysis. In: Proc Fifth Berkeley Symp. Math Statist. Prob. 1. University of California Press, pp. 401-413] is extended to more than one sequence of random variables. The Bayesian sequential estimation problem for one-parameter exponential families is considered and an asymptotically pointwise optimal rule, which includes a sequential allocation procedure and a stopping time, is provided. Some properties of asymptotic optimality are also obtained for the rules with and without using the prior information.

Suggested Citation

  • Hwang, Leng-Cheng & Karunamuni, Rohana J., 2008. "Asymptotically pointwise optimal allocation rules in Bayes sequential estimation," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2490-2495, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2490-2495
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    References listed on IDEAS

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    1. Rohana Karunamuni, 1996. "Empirical Bayes sequential estimation for exponential families: The untruncated component," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 711-730, December.
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    Cited by:

    1. Leng-Cheng Hwang & Chia-Chen Yang, 2015. "A robust two-stage procedure in Bayes sequential estimation of a particular exponential family," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 145-159, February.

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