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Asymptotic optimality of estimators in non-regular cases

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Summary

The bound of the asymptotic distributions of\(n\left| {\hat \theta _n - \theta } \right|\) for all asymptotically median unbiased (AMU) estimators\(\hat \theta _n \) is given in non-regular cases. It provides us with a powerful criterion for an AMU estimator to be two-sided asymptotically efficient and also useful in the cases when there may not exist a two-sided asymptotically efficient estimator since we may find an AMU estimator whose asymptotic distribution attains at least at a point, or an AMU estimator whose asymptotic distribution is uniformly “close” to it. Some examples are given.

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Authors and Affiliations

  1. University of Electro-Communications, Japan

    Masafumi Akahira

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  1. Masafumi Akahira
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Additional information

The results of this paper have been presented at the Meeting on Statistical Theory of Model Analysis at Tsukuba University in Japan, October 1979.

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Akahira, M. Asymptotic optimality of estimators in non-regular cases. Ann Inst Stat Math 34, 69–82 (1982). https://doi.org/10.1007/BF02481008

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  • DOI: https://doi.org/10.1007/BF02481008

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