Testing proportionality of two high-dimensional covariance matrices

Cheng，Guanghui1; Liu，Baisen2; Tian，Guoliang3; Zheng，Shurong4

2020-10-01

10.1016/j.csda.2020.106962

COMPUTATIONAL STATISTICS & DATA ANALYSIS   影响因子和分区

0167-9473

1872-7352

This article proposes three tests for proportionality hypotheses regrading high-dimensional covariance matrices. Compared with currently available tests in the literature that fail in situations involving a “large p small n” or require knowledge of the underlying normal distributions, these tests are nonparametric, and do not require specifying any known distribution to derive asymptotic distributions under both the null hypothesis as well as an alternative hypothesis. The theoretical justification for the proposed tests is provided to ensure their validity, especially when the number of dimensions p is larger than the sample size n. Numerical studies show that the proposed tests are adaptively powerful against dense as well as sparse alternatives for a wide range of dimensions and sample sizes. The tests were used to analyze a gene expression dataset to verify their effectiveness.

Covariance matrices Dense alternatives High-dimensional inference Proportionality test Sparse alternatives

SCI ; EI

英语

其他

National Natural Science Foundation of China[11690012][11522105] ; Department of Education of Liaoning Province, China[LN2017ZD001]

Computer Science ; Mathematics

Computer Science, Interdisciplinary Applications ; Statistics & Probability

WOS:000539101800016

ELSEVIER

20201908617230

Statistical tests ; Gene expression ; Sampling ; Normal distribution

Biology:461.9 ; Mathematics:921 ; Probability Theory:922.1 ; Mathematical Statistics:922.2

MATHEMATICS

2-s2.0-85084176860

Scopus

1.School of Economics and Statistics,Guangzhou University,Guangzhou,China
2.School of Statistics,Dongbei University of Finance and Economics,Dalian,China
3.Department of Statistics and Data Science,Southern University of Science and Technology,Shenzhen,China
4.School of Mathematics & Statistics and KLAS,Northeast Normal University,Changchun,China

Cheng，Guanghui,Liu，Baisen,Tian，Guoliang,et al. Testing proportionality of two high-dimensional covariance matrices[J]. COMPUTATIONAL STATISTICS & DATA ANALYSIS,2020,150.

Cheng，Guanghui,Liu，Baisen,Tian，Guoliang,&Zheng，Shurong.(2020).Testing proportionality of two high-dimensional covariance matrices.COMPUTATIONAL STATISTICS & DATA ANALYSIS,150.

Cheng，Guanghui,et al."Testing proportionality of two high-dimensional covariance matrices".COMPUTATIONAL STATISTICS & DATA ANALYSIS 150(2020).