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Minimax invariant estimator of a continuous distribution function

  • Estimation
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Abstract

Consider the problems of the continuous invariant estimation of a distribution function with a wide class of loss functions. It has been conjectured for long that the best invariant estimator is minimax for all sample sizes n≥1. This conjecture is proved in this short note.

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Authors and Affiliations

  1. Department of Applied Mathematics, State University of New York, 11794, Stony Brook, NY, U.S.A.

    Qiqing Yu

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  1. Qiqing Yu
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Additional information

Partially supported by National Science Foundation Grant DMS 9001194.

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Yu, Q. Minimax invariant estimator of a continuous distribution function. Ann Inst Stat Math 44, 729–735 (1992). https://doi.org/10.1007/BF00053401

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  • DOI: https://doi.org/10.1007/BF00053401

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