Tests for covariance matrices in high dimension with less sample size

Srivastava, M. S.; Yanagihara, Hirokazu; Kubokawa, Tatsuya

doi:10.1016/j.jmva.2014.06.003

Cited by 60 publications

(53 citation statements)

References 27 publications

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“…where Later, Srivastava and Yanagihara [45] and Srivastava et al [46] extended this work to the cases of two or more population covariance matrices and without normality assumptions, respectively. Furthermore, Cai and Ma [9] showed that T S1 is rate-optimal over this asymptotic regime, and Zhang et al [54] proposed the empirical likelihood ratio test for this problem.…”

Section: Ntm On Covariance Matricesmentioning

confidence: 96%

A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

Bai

2016

Sci. China Math.

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In this paper, we introduce the so-called naive tests and give a brief review of the new developments. Naive testing methods are easy to understand and perform robustly, especially when the dimension is large. In this paper, we focus mainly on reviewing some naive testing methods for the mean vectors and covariance matrices of high-dimensional populations, and we believe that this naive testing approach can be used widely in many other testing problems.

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Section: Ntm On Covariance Matricesmentioning

confidence: 96%

A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

Bai

2016

Sci. China Math.

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“…Next, we consider the high-dimensional cases, p > n, and compare the SS with the tests pro- Srivastava et al (2014). GCT is implemented using the function GCT.test in the R package "highD2pop" .…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem

Feng¹,

Zou²,

Wang³

2016

Journal of the American Statistical Association

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This article concerns tests for the two-sample location problem when data dimension is larger than the sample size. Existing multivariate-sign-based procedures are not robust against high dimensionality, producing tests with type I error rates far away from nominal levels. This is mainly due to the biases from estimating location parameters. We propose a novel test to overcome this issue by using the "leave-one-out" idea. The proposed test statistic is scalarinvariant and thus is particularly useful when different components have different scales in high-dimensional data. Asymptotic properties of the test statistic are studied. Compared with other existing approaches, simulation studies show that the proposed method behaves well in terms of sizes and power.

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“…We compare our proposed SST with the tests proposed by Srivastava et al [11] (SKK) and Chen and Qin [3] (CQ). Since the estimator of tr(R 2 ) used in the SKK procedure has a considerable bias under non-normal distributions, we use the estimator proposed by Srivastava et al [12] instead. For power comparison, we choose 1 = (σ ij ), σ ij = 0.5 |i−j| , and 2 = I p .…”

Section: Numerical Studiesmentioning

confidence: 99%

A simpler spatial-sign-based two-sample test for high-dimensional data

Wang

Zou

2016

Journal of Multivariate Analysis

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a b s t r a c tThis article concerns the tests for the equality of two location parameters when the data dimension is larger than the sample size. Existing spatial-sign-based procedures are not robust with respect to high dimensionality, producing tests with the type-I error rates that are much larger than the nominal levels. We develop a correction that makes the sign-based tests applicable for high-dimensional data, allowing the dimensionality to increase as the square of the sample size. We show that the proposed test statistic is asymptotically normal under elliptical distributions and demonstrate that it has good size and power in a wide range of settings by simulation.

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Tests for covariance matrices in high dimension with less sample size

Cited by 60 publications

References 27 publications

A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem

A simpler spatial-sign-based two-sample test for high-dimensional data

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