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Methodology for the invariant estimation of a continuous distribution function

  • Estimation
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Abstract

Consider both the calssical and some more general invariant decision problems of estimating a continuous distribution function, with the loss function {ie503-1} and a sample of sizen fromF. It is proved that any nonrandomized estimator can be approximated in Lebesgue measure by the more general invariant estimators. Some methods for investigating the finite sample problem are discussed. As an application, a proof that the best invariant estimator is minimax when the sample size is 1 is given.

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Authors and Affiliations

  1. Mathematics Department, Zhongshan University, the People's Republic of China

    Qiquing Yu

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  1. Qiquing Yu
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Yu, Q. Methodology for the invariant estimation of a continuous distribution function. Ann Inst Stat Math 41, 503–520 (1989). https://doi.org/10.1007/BF00050665

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  • DOI: https://doi.org/10.1007/BF00050665

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