A Shrinkage-based Self-normalization Test For Equality Of Mean Vectors In High-dimensional Data

With the rapid development of science and technology,high-dimensional data are commonly found in different fields of science and humanities.The analysis of high-dimensional data has brought new challenges to classical statistical methods.Taking the test of overall mean as an example,on the one hand,certain classical hypothesis testing statistics may be undefined when the dimensionality of data is much larger than the sample size.On the other hand,the limit theory of classical multivariate statistics usually assumes that the sample size is infinite but the number of dimensions is fixed.When the sample size and dimension tend to infinity at the same time,classical statistical methods may no longer be applicable.In this paper,we construct a self-normalized two-sample mean vector test statistic for the condition of "large p and small n" and give the limit distribution and theoretical statistical power of the statistic by combining the strong mixing sequence assumption and the shrinkage-based variance estimation method.The method effectively avoids the estimation of high-dimensional covariance matrices and can be applied to the problem of testing high-dimensional means.In terms of data adjustment,we give an approximate adjustment algorithm for sample strong mixed series and propose a new algorithm for the selection of window function.Compared with several other common tests,our proposed statistic exhibits a controllable Type I error rate and good empirical statistical efficacy under a wide range of data conditions.In real data tests,our method exhibits results consistent with other research results,which also illustrates the superiority of our proposed methods.