High-dimensional Variance Analysis

In recent decades, with the high-speed development of computer science and tech-nology, multiple statistical analysis is more and more important in the study of modern science. In many emerging areas, there are some high-dimensional data, however, the classical methods of multiple statistics fall behind the development of high-dimensional data. So we need some new methods of statistics to make up the deficiency of theory owing to the increasing of dimensions.This paper is mainly about the high dimensional variance analysis. In classical variance analysis,the dimension of the samples are low. Therefore,we use Wilk’s theory to get simulation of the statistics’asymptotic distribution. However, with the increasing of data dimension, classical methods are not suitable anymore. In this paper, we use large dimensional random matrix theory to study the high dimensional variance analysis. It gives us a method to use line spectrum statistic of F-matrix to check variance analysis of statistics. This method is not only suitable for low dimension but also suitable for high dimension. I also use matlab to simulate, it verifies the operationality of the method in this paper.