Normality Hypothesis Testing Of High-dimensional Data

The normal distribution is widely used in many statistical theories and methods due to its excellent properties,so it is necessary to test whether a dataset follows the normal distribution.In recent years,more and more practical problems use high-dimensional data,which made the normality hypothesis testing problem always full of vitality.This article starts with the univariate normality tests and summarizes the basic principles,advantages and disadvantages,and applicable data types of the four major test.In this paper,the normality testing methods of high-dimensional data are divided into four categories: statistical chart testing,multiple univariate testing,suitable dimensionality reduction methods,and direct testing of high-dimensional data.In addition,this article summarizes how the univariate normality test is extended to the high-dimensional case.Then the performances of various high-dimensional normality testing methods are compared through computer simulations.The conclusions include: some high-dimensional normality tests can't control the type I error,one of the effective strategies is increasing the ratio of sample size and dimension;the HZ test and the JB test after independent transformation performed best,etc.Finally,this paper tests the normality of the two actual datasets,and the results are both rejecting the null hypothesis,which shows the necessity of verifying the normality hypothesis condition in actual research.