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Information Inequalities in a Family of Uniform Distributions

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Abstract

For a family of uniform distributions, it is shown that for any small ε < 0 the average mean squared error (MSE) of any estimator in the interval of Θ values of length ε and centered at Θ0 can not be smaller than that of the midrange up to the order o(n −2) as the size n of sample tends to infinity. The asymptotic lower bound for the average MSE is also shown to be sharp.

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References

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Authors and Affiliations

  1. Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan

    Masafumi Akahira

  2. Faculty of International Studies, Meiji-Gakuin University, Kamikurata-cho 1598, Totsuka-ku, Yokohama, 244-0816, Japan

    Kei Takeuchi

Authors
  1. Masafumi Akahira
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  2. Kei Takeuchi
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Akahira, M., Takeuchi, K. Information Inequalities in a Family of Uniform Distributions. Annals of the Institute of Statistical Mathematics 53, 427–435 (2001). https://doi.org/10.1023/A:1014685808327

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  • DOI: https://doi.org/10.1023/A:1014685808327

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