AIC-TYPE MODEL SELECTION CRITERION FOR MULTIVARIATE LINEAR REGRESSION WITH A FUTURE EXPERIMENT

抄録

This paper deals with the situation in which a current experiment is given and although a future design matrix has been prepared, the corresponding observation matrix is not available. To predict the future observation matrix, we consider selecting an appropriate design matrix by proposing a predictive Akaike Information Criteria (PAIC). The PAIC is derived as an exact unbiased estimator for the risk function and is based on the expected Kullback-Leibler divergence and the future design matrix. A simulation study illustrated that model selection with PAIC performs well for some extrapolation cases.