Simulationâ€ based hypothesis testing of high dimensional means under covariance heterogeneity
Wenâ€ Xin Zhou and
Biometrics, 2017, vol. 73, issue 4, 1300-1310
In this article, we study the problem of testing the mean vectors of high dimensional data in both oneâ€ sample and twoâ€ sample cases. The proposed testing procedures employ maximumâ€ type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose twoâ€ step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic data sets and an human acute lymphoblastic leukemia gene expression data set, we illustrate the performance of the new tests and how they may provide assistance on detecting diseaseâ€ associated geneâ€ sets. The proposed methods have been implemented in an Râ€ package HDtest and are available on CRAN.
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Persistent link: https://EconPapers.repec.org/RePEc:bla:biomet:v:73:y:2017:i:4:p:1300-1310
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