Minimaxity and nonminimaxity of a preliminary test estimator for the multivariate normal mean |
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Authors: | Taichi Inaba Yasushi Nagata |
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Institution: | (1) Osaka University, Osaka, Japan;(2) Present address: Nagoya University, Nagoya, Japan |
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Abstract: | Summary The problem is to estimate the mean of ap-dimensional normal distribution in the situation where there is vague information that the mean vector might be equal to
zero vector. Minimax property of the preliminary test estimator obtained by the use of AIC (Akaike's Information Criterion)
procedure is discussed under a loss function which is based on Kullback-Leibler information measure and evaluates both an
error of model selection and that of estimation. Whenp is even, the minimaxity is shown to hold for small values ofp but not for large values. |
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Keywords: | Preliminary test estimator minimaxity AIC Kullback-Leibler information measure |
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