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Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity. / Chang, Jinyuan; Zheng, Chao; Zhou, Wen-Xin et al.
In: Biometrics, Vol. 73, No. 4, 12.2017, p. 1300-1310.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Chang, J, Zheng, C, Zhou, W-X & Zhou, W 2017, 'Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity', Biometrics, vol. 73, no. 4, pp. 1300-1310. https://doi.org/10.1111/biom.12695

APA

Chang, J., Zheng, C., Zhou, W-X., & Zhou, W. (2017). Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity. Biometrics, 73(4), 1300-1310. https://doi.org/10.1111/biom.12695

Vancouver

Chang J, Zheng C, Zhou W-X, Zhou W. Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity. Biometrics. 2017 Dec;73(4):1300-1310. Epub 2017 Mar 31. doi: 10.1111/biom.12695

Author

Chang, Jinyuan ; Zheng, Chao ; Zhou, Wen-Xin et al. / Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity. In: Biometrics. 2017 ; Vol. 73, No. 4. pp. 1300-1310.

Bibtex

@article{53609a1762a0401380920727654fc092,
title = "Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity",
abstract = "In this article, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-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 two-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 disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN.",
keywords = "Feature screening, High dimension, Hypothesis testing, Normal approximation, Parametric bootstrap, Sparsity",
author = "Jinyuan Chang and Chao Zheng and Wen-Xin Zhou and Wen Zhou",
year = "2017",
month = dec,
doi = "10.1111/biom.12695",
language = "English",
volume = "73",
pages = "1300--1310",
journal = "Biometrics",
issn = "0006-341X",
publisher = "Wiley-Blackwell",
number = "4",

}

RIS

TY - JOUR

T1 - Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity

AU - Chang, Jinyuan

AU - Zheng, Chao

AU - Zhou, Wen-Xin

AU - Zhou, Wen

PY - 2017/12

Y1 - 2017/12

N2 - In this article, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-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 two-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 disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN.

AB - In this article, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-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 two-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 disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN.

KW - Feature screening

KW - High dimension

KW - Hypothesis testing

KW - Normal approximation

KW - Parametric bootstrap

KW - Sparsity

U2 - 10.1111/biom.12695

DO - 10.1111/biom.12695

M3 - Journal article

VL - 73

SP - 1300

EP - 1310

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 4

ER -