DATA-COMPATIBLE MODEL SELECTION AND A MINIMAX FAMILY OF MODEL SELECTION AND ESTIMATION PROCEDURES FOR A MULTIVARIATE NORMAL MEAN

抄録

The inference procedure for the mean vector of a p-dimensional normal distribution with known variance-covariance matrix is considered under a loss function which evaluates both the error of model selection and that of estimation. The concept of “data-compatible model selection” is introduced. It is shown that procedures with data-compatible model selection and estimation by maximum likelihood estimator (m. l. e.) form a minimax family and that procedures with data-incompatible model selection and estimation by m. l. e. are not minimax.