Inference Of High-Dimensional Data Based On Extended Cross-Data-Matrix And Two-Stage Method

In recent years,high-dimensional data has appeared more and more widely in various scientific fields.A typical feature of high-dimensional data is that the data dimension p is large and the sample size n is relatively small,that is,high-dimensional small sample capacity.Many statisticians pay attention to the problem of hypothesis testing of high-dimensional population mean vectors,and there are fewer problems in determining the sample size of high-dimensional populations.This paper discusses the parameter estima-tion of the mean vector of the high-dimensional population and the determination of the sample size in the hypothesis test problem.In view of this problem,there are two main tasks in this paper,as follows:One,in chapter 3,in the case of unequal covariance matrices,discuss the hypothesis test of k linear combinations of high-dimensional mean vectors and the determination of sample size.This chapter first gives the statistics used for construction inspection,and uses a two-stage procedure and the Extended Cross-Data-Matrix(ECDM)method to discuss the determination of the sample size.Second,the asymptotic distribution of the proposed statistics is discussed using the martingale difference center limit theorem.Finally,simulation studies show that the sample size determined in this chapter meets the given accuracy,and an example is given to show that the method for determining the sample size in this chapter is reasonable and effective under the proposed assumptions.Two,in chapter 4,the confidence region of a given radius for the mean vector estima-tion is discussed,and the determination of the sample size is discussed using a two-stage procedure and an ECDM method.First,based on the assumption that the eighth-order moment of each sample component is no longer consistent and bounded,it is determined that the sample capacity meets the predetermined accuracy.Then the simulation pro-gram results are compared with the sample size determined by the Cross-Data-Matrix(CDM)method,and examples are given to show that under the assumptions mentioned,the method for determining the sample size in this chapter is reasonable and effective.