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 2^p 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.