High-dimensional AICs for selection of variables in discriminant analysis.

This paper is concerned with high-dimensional modifications of Akaike information criterion (AIC) for selection of variables in discriminant analysis. The AIC has been proposed as an asymptotically unbiased estimator of the risk function of the candidate model when the dimension is fixed and the sample size tends to infinity. On the other hand, Fujikoshi () attempted to modify the AIC in two-group discriminant analysis when the dimension and the sample size tend to infinity. Such an estimator is called high-dimensional AIC, which is denoted by HAIC. However, its modification was obtained under a restrictive assumption, and furthermore, it was difficult to extend the method to multiple-group case. In this paper, by a new approach we propose HAIC which is an asymptotically unbiased estimator of the risk function in multiple-group discriminant analysis when both the dimension and the sample size tend to infinity, for a general class of candidate models. By simulation experiments it is shown that HAIC is more useful than other AIC type of criteria. [ABSTRACT FROM AUTHOR]