Hypothesis Test Of High-dimensional Nonparametric Behrens-Fisher Problem Based On Bootstrap Method

With the rapid development of science and technology,human society has ush?ered in the era of "big data",and high-dimensional data has appeared in many fields.However,traditional statistical methods cannot be simply applied to high-dimensional data,so we need to find new statistical methods to study and process these data.When studying the non-parametric Behrens-Fisher problem,the exist-ing test methods,such as O'brien's rank sum test,modified O'Brien's rank sum test and maximum rank test,are all researches on the theory of asymptotic distribution under low-dimensional data,so there is currently no good way to perform hypothesis testing in the case of high-dimensional data.Based on this,this thesis proposes a new test statistic to perform hypothesis testing on the non-parametric Behrens-Fisher problem under high-dimensional data.In the case of high-dimensional data,new statistics are required to derive more ac-curate mean estimation and covariance.Estimation is more difficult,so this article uses the Stationary Bootstrap method to test the statistical properties of the new statistic,and proposes an algorithm to calculate the p-value of the new test statistic using the Stationary Bootstrap method,thereby avoiding the complicated process of deriving the mean estimation and the covariance estimation.Through a large number of data simulation experiments by R language and comparison with the simulation results of the O'Brien rank sum test,the modified O'Brien rank sum test and the maximum rank test.we find that the test statistics proposed in this the-sis are more suitable for high-dimensional non-parametric Behrens-Fisher problem because of the better first type of error and the good test power.