Mean Text Of K High-dimensional Population Under Behrens-Fisher Setting

In recent years,with the rapid development of data collecting technologies,high dimensional data have become increasingly prevalent.Much work has been done for test-ing hypotheses on mean vectors,especially for high-dimensional two-sample problem.Rather than considering a specific problem,we focus the equality of several high dimen-sional mean vectors with unequal covariance matrices,this is one of the most important problems in multivariate statistical analysis.In response to this problem,there are two main work of this thesis,as follows:One,in chapter 3,we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices.We propose a new scalar and shift transform invariant test statistic for the high-dimensional k-sample location problem.Proved that our statistic asymptotically normal distribution is proved by the method of the martingale differece center limit theorem.Theoretical results and simulation studies show that the proposed test statistic has good properties under certain circumstances.Two,in chapter 4,a k-sample test statistic is presented for testing the equality of mean vectors when the dimension p exceeds the sample sizes,or the dimension and sample size tend to infinity and the distribution are not necessarily normal.Whether the sample sizes and covariance matrices are assumed equal or not,i.e.,under Behrens-Fisher setting.Our statistic is an approximate normal distribution using the asymptotic theory of degenerate U-statistics and the classical central limit theorem.In addition,the simulation study proves that the U-statistic method used in this chapter is better than the martingale differece center limit theorem.