Takayuki Yamada: Statistical inference concerning normal based discriminant analysis when the dimension is large compared to sample sizes

Statistical inference about discriminant analysis of two groups are given under the assumption of multi-dimensional normality for population distribution. The result is based on the asymptotic that the sample sizes tend to infinity. However, the precision of the asymptotic approximation gets worse for the case that the dimension is comparatively large. High-dimensional asymptotic framework is reported as a way to improve the accuracy (One of literatures is Fujikoshi, Ulyanov and Shimizu [2010]). High-dimensional asymptotic framework is that the dimensionality and sample sizes tend to infinity together. In this seminar, I will talk about 2 topics. One is about the estimation of miss classification probability. The other is about confidence interval of log odds ratio for the posterior probabilities. These results are obtained under high-dimensional asymptotic framework.