Piecewise Test Of The Normal Population Hypothesis Problem Under High-dimensional Dat

In recent years,researchers have collected and stored more and more high-dimensional data in application fields such as hyperspectral images,Internet portals,radio communication signal networks and stock market analysis,therefore,the research on high-dimensional data has also become crucial.Under high-dimensional data,the traditional test statistics of mean test and multivariate analysis of variance are not defined.In this paper,a piecewise and stepwise test method is proposed to solve the problem of invalidation of traditional test statistics caused by high-dimensional data.The first chapter introduces the research background,significance and current situation of the mean test and multivariate analysis of variance under high-dimensional data,and briefly describes some new statistics and their asymptotic distribution properties obtained by scholars at home and abroad by modifying the traditional test statistics.The second chapter tests the mean value test in the case of a single normal population step by step.The mean vector is divided into k parts,so that the dimension of each part of the variable is smaller than the sample size,and at the same time,try to reduce the loss of correlation between variables.Then,the Hotelling T~2test statistics are used to test each part in turn.The test ends when the first result rejects the original hypothesis and considers the entire hypothesis rejected.At the same time,a new method to control the probability of making the first type of error is given.Through data simulation,the probability of making the first type of error can be stabilized around the predefined significance level.The third chapter gives the piecewise test method of the mean test problem in the case of two normal populations.When the covariance matrices of the two populations are equal,the mean vector is still segmented and then tested by Hotelling T~2test;when the covariance matrices of the two populations are not equal,after dividing the mean vectors of the two populations,the mean test problem of the two populations is transformed into the mean test problem of a single population for testing by properly transforming each part of the random vector.When the covariance matrices of the two populations are unequal,the method of using the generalized p value to test the mean vectors is also given,the mean vectors are segmented and tested successively by the generalized p value.The forth chapter gives a piecewise test method for multivariate analysis of variance.We divide the unknown parameter matrix into k parts,and then use Wilks test statistics to test each part of the variables in turn.We use Monte Carlo method to simulate the data,the simulation result display that this test method can control the probability of making the first type of error at a given significance level.