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A characterization of second order efficiency in a curved exponential family

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Summary

The optimality of estimation method is investigated in a curved exponential family. A risk function, which is an extension of a residual sum of squares in regression analysis, is introduced. It is shown that second order efficiency of an estimation method is equivalent to attain the minimum among limiting risks of all estimation methods.

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References

  1. Amari, S. (1982). Differential geometry of curved exponential families-curvature and information loss,Ann. Statist.,10, 357–385.

    Article  MathSciNet  Google Scholar 

  2. Drossos, C. A. and Phillipou, A. N. (1980). A note on minimum distance estimates,Ann. Inst. Statist. Math.,32, A, 121–123.

    Article  MathSciNet  Google Scholar 

  3. Efron, B. (1982). Maximum likelihood and decision theory,Ann. Statist.,10, 340–356.

    Article  MathSciNet  Google Scholar 

  4. Eguchi, S. (1983). Second order efficiency of minimum contrast estimators in a curved exponential family,Ann. Statist.,11, 793–803.

    Article  MathSciNet  Google Scholar 

  5. Eguchi, S. (1984). A property of second order efficiency,Technical Report, No. 132, Statistical Research Group, Hiroshima University.

  6. Ghosh, J. K. and Subramanyam, K. (1974). Second order efficiency of maximum likelihood estimators,Sankhyā, A,36, 325–358.

    MathSciNet  MATH  Google Scholar 

  7. Kuboki, H. (1982). Unbiased estimations in the sense of Lehmann and their discrimination rates,Ann. Inst. Statist. Math., A,34, 19–37.

    Article  MathSciNet  Google Scholar 

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  1. Shinto Eguchi

    Present address: Hiroshima University, Hiroshima, Japan

Authors and Affiliations

  1. Osaka University, Osaka, Japan

    Shinto Eguchi

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  1. Shinto Eguchi
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Eguchi, S. A characterization of second order efficiency in a curved exponential family. Ann Inst Stat Math 36, 199–206 (1984). https://doi.org/10.1007/BF02481964

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  • DOI: https://doi.org/10.1007/BF02481964

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