The Kullback-Leibler risk of the Stein estimator and the conditional MLE |
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Authors: | Takemi Yanagimoto |
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Institution: | (1) The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106 Tokyo, Japan |
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Abstract: | The decomposition of the Kullback-Leibler risk of the maximum likelihood estimator (MLE) is discussed in relation to the Stein estimator and the conditional MLE. A notable correspondence between the decomposition in terms of the Stein estimator and that in terms of the conditional MLE is observed. This decomposition reflects that of the expected log-likelihood ratio. Accordingly, it is concluded that these modified estimators reduce the risk by reducing the expected log-likelihood ratio. The empirical Bayes method is discussed from this point of view. |
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Keywords: | Conditional inference empirical Bayes method expected log-likelihood ratio exponential dispersion model maximum likelihood estimator Stein estimator |
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