The High-dimensional Mean And The Median Deviation Of The Covariance Matrix Test Statistic

With the explosive growth of global data volume,it has been widely used in com-putational biology,medicine,financial analysis and risk control.Especially in the fields of bioinformatics and financial management,the dimension of experimental data is even larger than the size of samples.At this time,large data is represented as high-dimensional data problem.In recent years,high-dimensional data analysis has become one of the hot research fields in statistics.A large number of remarkable research results have emerged,which has greatly promoted the reform and development of statistical ideas and methods.Moderate deviation and large deviation are important branches of probability limit theory.Their essential theories originate from the study of Donsker and Varadhan.Devi-ation theory is also widely used in practical problems,such as stochastic disturbance of dynamic systems,financial statistics and insurance,partial differential,etc.The research of various scholars in the field of high-dimensional data provides us with a new environ-ment.With the improvement of the theorem of large number and central limit theorem,large deviation and moderate deviation also provide us with new challenges.Therefore,based on high-dimensional data,this paper discusses the moderate devi-ation problem of test statistics of high-dimensional mean and covariance matrix in two cases of sample independence or dependence.The paper is divided into three chapters,the main contents are as follows:The first chapter mainly states the research background of this paper,reviews the rel-evant knowledge and theory used in this paper,gives the definition of moderate deviation and large deviation,and finally lists the main work of this paper.In the second chapter discusses the problem of moderate deviation of test statistics for high-dimensional covariance matrix.In the case of sample independence,the Gartner-Eillis theorem is used to obtain that test statistics satisfy the principle of moderate devi-ation.Data simulation is also given to verify that the test statistics satisfy the results of moderate deviation when samples obey normal distribution and gamma distribution.The third chapter studies the mean value of high-dimensional data,and discusses the deviation of test statistics in the case of sample dependence under the hypothesis test problem.