Testing Equality Of Several High-dimensional Sample Correlation Matrices

In recent decades, with the high speed development of computer science and tech-nology, it is possible to collect, store and analyze high dimensional data. In multivariate statistical analysis, statistical inference for high dimensional covariance matrix becomes more and more important. When the dimension and sample size tend to infinity, many classical statistical theories become invalid. Therefore, some new high dimensional meth-ods need to be proposed.Sample correlation matrix is an important random matrix in multivariate statistical analysis, especially for testing covariance structures, principal component analysis and factor analysis etc. This thesis is to extend testing equality of two high dimensional correlation matrices (Li, Zheng and Zheng,2016) to testing equality of several high di-mensional correlation matrices. Moreover, some simulations and a real data analysis are conducted in this thesis.