Hypothesis Testing Of Normal Populations With High-dimensional Data

With the rapid development of computer science and technology,human beings have entered the era of big data.Data collection is becoming easier and easier.At the same time,the scale and complexity of database are becoming larger and larger,presenting high-dimensional data,This kind of data widely exists in the fields of Biostatistics,meteorological statistics,agriculture,finance and so on.In multivariate statistical analysis,many classical test methods fail under the background of high-dimensional data.In order to solve this problem,this paper studies a series of hypothesis testing problems about normal population under high-dimensional dataIn the first chapter,we introduce the related research and development process of the test problem under high-dimensional data,and briefly introduce the related theorems and preparatory knowledge to be used in the following.In the second chapter,we use Bonferroni correction to study the hypothesis test of the mean value of normal distribution under high-dimensional data.We propose a new method to divide the sample matrix according to the dimension.Combined with the classical Hotelling~2test method,we discuss the single sample case and the double sample case respectively,and obtain the new test statistics,Numerical simulation shows that the test is good.In the third chapter,based on the likelihood ratio,combining with the union-intersection principle,we study the ANOVA under high-dimensional data.We give the generalized likelihood ratio statistics of the test and its related properties,and simulate the test level with Monte Carlo method.The results show that the test can control the test level well.In the fourth chapter,based on the likelihood ratio and the principle of intersection,we study the hypothesis testing problem of linear constraint of normal mean under high-dimensional data.We give a new definition of the generalized likelihood ratio statistics and its related properties.The data simulation method is used to verify that the test can better control the test level than Bai and saranadasa's test method.In the fifth chapter,based on the likelihood ratio and the principle of intersection,we study the independence test of random variables in high-dimensional data.We focus on the independence test of two groups of variables in high-dimensional data,and propose the definition,theorem and test method.