Hypothesis Tests Of Mean Vectors And Covariance Matrices In High-dimensional Data

This dissertation studies two hypothesis test problems in high-dimensional setting.One is the hypothesis test about the linear combinations of k-sample mean.The other is to test the hypothesis simultaneously about mean vector and covariance matrix.The full text is divided into four chapters.In Chapter 1,we introduce some existing test procedures on mean vectors and covariance matrices under high-dimensional and super-high-dimensional data.In Chapter 2,our aim is to test the hypothesis about the linear combinations of k-sample mean vectors in normal models with heteroskedasticity when data dimensional is larger than sample size.The motivation is on the basis of the generalized likelihood ratio method and the Bennett transformation.We propose a new test procedure and obtain the asymptotic distribution of the new test under null and local alternative,respectively.The simulation results show that our proposed test outperforms some existing tests in many cases.In Chapter 3,we study the problem of simultaneous test on the mean vector and the covariance matrix in high-dimensional setting.A new test procedure is proposed,the asymptotic distributions of which are gotten under null and local alternative,re-spectively,with respect to mild conditions.The simulation demonstrates that our test can control satisfactorily the nominal level and has greater powers than the competing tests in many cases.The conclusion problems of this dissertation and farther problems are arranged in Chapter 4.