MINIMAXITY AND INADMISSIBILITY OF THE MODEL SELECTION AND ESTIMATION PROCEDURE FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION

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  • Nagata Yasushi
    Department of Applied Mathematics, Faculty of Engineering Science, Osaka University

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  • Minimaxity and Inadmissibility of the M

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Abstract

The inference procedure for the mean vector of a p-dimensional normal distribution with known variance-covariance matrix is discussed under a loss function which is based on the Kullback-Leibler information measure and evaluates both an error of model selection and that of estimation. The procedure which selects a model among 2p competing models by AIC (Akaike's Information Criterion) and then uses the maximum likelihood estimator under the chosen model is shown to be always minimax but inadmissible when p≥3.

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