Testing Homogeneity Of Covariance Matrices Of Several High-dimensional Populations

In recent years,with the development of computer science and technology,large dimensional data become available in many fields,such as biological microarray,fi-nancial analysis and quality control.However,the classical statistical methods are based on the assumption that the sample size n is much larger than the dimension p.Therefore,to apply such method to analyze large dimensional data will be in severe errors.Hence new statistical methods must be developed.In this thesis,we first propose a new method to test homogeneity of covariance matrices for high dimensional data using U-statistic.After that,a new hypothesis test is provided on the linear combinations of covariance matrices.These tests are based on framework that the sample size n and the dimension p are comparable,both tending to infinity which remedies the defect when the dimension increases.Then asymptotic dis-tributions under null hypotheses are derived and the asymptotic properties of statistics are proved.Good performance of our statistics justified by simulation results when the di-mension is relatively small(p = 32)or considerably large(p = 256).Especially when classical methods and the comparative methods do not work well or even do not work,the type I errors of our methods are very close to the predefined test level,and the powers increase to 1 quickly.In linear model theory,a series of assumptions are needed,one of which is the knowledge of error term in order to derive the distribution of dependent variable.To this end,test of the homogeneity of multiple linear models of error terms for high-dimension is introduced at the end of this thesis.It is worth mentioning that we do not impose restrictions on distributions of data.