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Estimators for the binomial distribution that dominate the MLE in terms of Kullback–Leibler risk

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Abstract

Estimators based on the mode are introduced and shown empirically to have smaller Kullback–Leibler risk than the maximum likelihood estimator. For one of these, the midpoint modal estimator (MME), we prove the Kullback–Leibler risk is below \({\frac{1}{2}}\) while for the MLE the risk is above \({\frac{1}{2}}\) for a wide range of success probabilities that approaches the unit interval as the sample size grows to infinity. The MME is related to the mean of Fisher’s Fiducial estimator and to the rule of succession for Jefferey’s noninformative prior.

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Authors and Affiliations

  1. Department of Biostatistics, East Carolina University, Greenville, NC, 27858, USA

    Paul Vos & Qiang Wu

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  1. Paul Vos
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  2. Qiang Wu
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Correspondence to Paul Vos.

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Vos, P., Wu, Q. Estimators for the binomial distribution that dominate the MLE in terms of Kullback–Leibler risk. Ann Inst Stat Math 64, 359–371 (2012). https://doi.org/10.1007/s10463-010-0316-3

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  • DOI: https://doi.org/10.1007/s10463-010-0316-3

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