A New Statistical Method For The Comparison Of Two Samples In High-dimensional Population

With the advancement of science and the development of society,statistics are particularly important in the current environment.One of the very important components is multivariate statistics.For example,when it comes to the data in genetic analysis,in many cases we can directly or indirectly generalize the tested problem to the comparison of two mean vectors of high-dimensional data.When the data dimensions are much smaller than the number of samples,Hotelling T2 test had been proved to be efficient.However when it comes to the situation,which the data dimensions that are much larger than the sample size,its efficacy has not been guaranteed,and some scholars have finished the related research.They are mainly divided into two aspects.One of the method is comparing the sum of the differences of all elements of two vectors(usually the sum of the squares of the differences).The other one is based on the maximum form.In this paper,we first introduce two types of tests that are representative of these two methods:Srivastava(2013)and Cai(2014),and then we propose a test method based on the sum of squares of the largest and the smallest column components.It is used to test the vector equivalence of high-dimensional data in the case of sparse two samples.This method uses the information of different directions for the maximum and minimum column component,and it is expected to obtain greater power than the existing methods.And the method has been proved theoretically.Under some regular conditions,the asymptotic distribution of the method is obtained.Then we do a lot of computer simulation of these three methods.Finally,by analyzing the real data of gene expression with age,the superiority of our proposed method is verified.