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Asymptotic non-deficiency of the Bayes sequential estimation in a family of transformed Chi-square distributions

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Abstract

Bayes sequential estimation in a family of transformed Chi-square distributions using a linex loss function and a cost c > 0 for each observation is considered in this paper. It is shown that an asymptotic pointwise optimal rule (A.P.O.) is asymptotically non-deficient, i.e., the difference between the Bayes risk of the A.P.O. rule and the Bayes risk of the optimal procedure is of smaller order of magnitude than c, the cost of single observation, as c → 0.

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  1. Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran

    Eisa Mahmoudi

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  1. Eisa Mahmoudi
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Correspondence to Eisa Mahmoudi.

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Mahmoudi, E. Asymptotic non-deficiency of the Bayes sequential estimation in a family of transformed Chi-square distributions. Metrika 75, 567–580 (2012). https://doi.org/10.1007/s00184-011-0342-z

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  • DOI: https://doi.org/10.1007/s00184-011-0342-z

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