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Second order optimal approximation in a particular exponential family under asymmetric LINEX loss

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  • Hwang, Leng-Cheng

Abstract

In this paper, we consider the problem of sequentially estimating the unknown parameter in a particular exponential family of distributions under an asymmetric LINEX loss function and fixed cost for each observation within a Bayesian framework. Under a gamma prior distribution, the second order approximation for the Bayes risks of the asymptotically pointwise optimal rule and the optimal stopping rule are derived. It is shown that the asymptotically pointwise optimal rule is asymptotically non-deficient in the sense of Woodroofe (1981).

Suggested Citation

  • Hwang, Leng-Cheng, 2018. "Second order optimal approximation in a particular exponential family under asymmetric LINEX loss," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 283-291.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:283-291
    DOI: 10.1016/j.spl.2018.01.032
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    References listed on IDEAS

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    1. Eisa Mahmoudi, 2012. "Asymptotic non-deficiency of the Bayes sequential estimation in a family of transformed Chi-square distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(4), pages 567-580, May.
    2. Alicja Jokiel-Rokita, 2011. "Bayes sequential estimation for a particular exponential family of distributions under LINEX loss," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 211-219, September.
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    Cited by:

    1. Hwang, Leng-Cheng, 2020. "A robust two-stage procedure for the Poisson process under the linear exponential loss function," Statistics & Probability Letters, Elsevier, vol. 163(C).

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