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Loss of information of a statistic for a family of non-regular distributions, II: more general case

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  • Masafumi Akahira
  • Hyo Kim
  • Nao Ohyauchi

Abstract

In the paper of Akahira (Ann Inst Statist Math 48:349–364, 1996 ), it was shown that the second order asymptotic loss of information in reducing to a statistic consisting of extreme values and an asymptotically ancillary statistic vanished for a family of non-regular distributions whose densities have the same values and the sum of differential coefficients at the endpoints of the bounded support is equal to zero. In this paper, the result can be shown to be extended to the case of a family of non-regular distributions without the above restriction. Copyright The Institute of Statistical Mathematics, Tokyo 2012

Suggested Citation

  • Masafumi Akahira & Hyo Kim & Nao Ohyauchi, 2012. "Loss of information of a statistic for a family of non-regular distributions, II: more general case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1121-1138, December.
    • Handle: RePEc:spr:aistmt:v:64:y:2012:i:6:p:1121-1138
    DOI: 10.1007/s10463-011-0347-4
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    References listed on IDEAS

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    1. Masafumi Akahira & Nao Ohyauchi & Kei Takeuchi, 2007. "On the Pitman estimator for a family of non-regular distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 113-127.
    2. Masafumi Akahira, 1996. "Loss of information of a statistic for a family of non-regular distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 349-364, June.
    3. Masahito Hayashi, 2010. "Limiting behavior of relative Rényi entropy in a non-regular location shift family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(3), pages 547-569, June.
    4. Masafumi Akahira, 1991. "The 3/2th and 2nd order asymptotic efficiency of maximum probability estimators in non-regular cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 181-195, March.
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