Simulation Comparisons Study About The Powers Of Several High-dimensional Mean Test

Multivariate mean test is an important component of the test in classic statis-tics.We often use the mean test to determine whether the newly developed drug is more effective,and we can use the test result to judge whether the new drug is significantly better than the previous drug.Drug development is supported by scien-tific decisions that provide statistical support.In classical statistics,the commonly used method for the mean test is the Hotelling-T2 test,The test method was proposed by Hotelling in 1931.A detailed proof of the distribution of statistics was given by Bowker.This method has a better power when the sample size is much larger than the variable.With the development of science,the data dimension we are facing is getting higher and higher,such as millions of gene locus was sequenced in genome-wide association analysis.In some cases,even when the variable dimen-sion is larger than the sample size in the high-dimensional data,it is not difficult to find the inverse of the covariance due to the composition of the Hotelling-T2 statistic does not exist,so Hotelling-T2 does not apply to tests where the vari-able dimension is larger than the sample size data.To solve this average-value test where the dimensions of the high-dimensional data are higher than the sample size,in recent decades some new methods was proposed to solve this problem.For ex-ample,in 1960 Dempster used an orthogonal transformation of the data matrix to construct an approximate F distribution and proposed an non-exact test method.In 1996,Bai Zhidong estimated the expectation and variance of NX'X-trS then he use the central limit theorem to test the normal approximation structure.In 2006 MuniS.Srivastava added the reciprocal of the variance diagonal is weighted to the sum of the squares of the mean values of the sample matrix,so that the distribu-tion converges to the standard normal distribution.After performing a simulation comparison,MuniS.Srivastava makes the test method perform better by adding an adjustment coefficient.This paper performs a large number of simulations by computer then gives the power results of several methods.In the simulation using R software,by changing the covariance generated sample data,change the dimensions and number of data,select a good alternative hypothesis simulation.Make a good record of the simulation and compare the simulation results to analyze the powers of these test methods under specific conditions.Analyze the power comparison of several methods based on a large number of simulation results.The performance of these methods in detail,to give firm conclusions relevant for researchers to use.