A TEST OF ADDITIONAL ACCURACY FOR SELECTING GROUPS OF ALLOCATION VARIABLES

The standardized difference in estimated Bayes risk between two subset s of groups of allocation variables is proposed as a test statistic fo r additional classification accuracy. This test is used in a minimal-b est-subset algorithm that aims to select the optimal subset for the da ta at hand-that is, the smallest subset retaining most of the classifi cation accuracy. A multivariate normal example confirms that all-possi ble-subsets and minimal-best discrimination procedures based on Wilks' s lambda and Rao's test usually do not identify the best subsets accor ding to estimated Bayes risk. The minimal-best discrimination subset w as suboptimal in all of 100 bootstrapped samples: It contained too man y groups in every case. In contrast, the minimal-best classification s elected an optimal subset for 82 out of 100 bootstrap examples; append ing a test of additional accuracy of the minimal-best subset versus th e overall-best subset led to an optimal subset in the other 18 cases b y suggesting the addition of more groups.