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A robust two-stage procedure in Bayes sequential estimation of a particular exponential family

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Abstract

The problem of Bayes sequential estimation of the unknown parameter in a particular exponential family of distributions is considered under linear exponential loss function for estimation error and a fixed cost for each observation. Instead of fully sequential sampling, a two-stage sampling technique is introduced to solve the problem in this paper. The proposed two-stage procedure is robust in the sense that it does not depend on the parameters of the conjugate prior. It is shown that the two-stage procedure is asymptotically pointwise optimal and asymptotically optimal for a large class of the conjugate priors. A simulation study is conducted to compare the performances of the two-stage procedure and the purely sequential procedure.

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Acknowledgments

This research was supported by the Ministry of Science and Technology of R.O.C. The authors are grateful to the editor and the referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Statistics, Tunghai University, Taichung, Taiwan, R.O.C.

    Leng-Cheng Hwang

  2. Department of Finance, Ling Tung University, Taichung, Taiwan, R.O.C.

    Chia-Chen Yang

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  1. Leng-Cheng Hwang
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  2. Chia-Chen Yang
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Correspondence to Leng-Cheng Hwang.

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Hwang, LC., Yang, CC. A robust two-stage procedure in Bayes sequential estimation of a particular exponential family. Metrika 78, 145–159 (2015). https://doi.org/10.1007/s00184-014-0493-9

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  • DOI: https://doi.org/10.1007/s00184-014-0493-9

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