More powerful tests for sparse high-dimensional covariances matrices

Peng, Liuhua; Chen, Song Xi; Zhou, Wen

doi:10.1016/j.jmva.2016.03.008

Cited by 11 publications

(5 citation statements)

References 38 publications

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“…Peng et al [35] improved the power of the test T τ QC by employing the banding estimator for the covariance matrices. Zhang et al [54] also gave the empirical likelihood ratio test procedure for testing whether the population covariance matrix has a banded structure.…”

Section: Ntm On Covariance Matricesmentioning

confidence: 99%

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: 99%

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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“…Some recent tests for bandedness can be found in [14], where a method for estimating matrix bandwidth is presented. Peng et al developed several tests for sparse high-dimensional covariance matrices [15]. In [9], An et al proposed test statistics for detecting band size and applied them to cancer data analysis.…”

Section: Introductionmentioning

confidence: 99%

Complex Parameter Rao and Wald Tests for Assessing the Bandedness of a Complex-Valued Covariance Matrix

Zhu

2024

Signals

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Banding the inverse of a covariance matrix has become a popular technique for estimating a covariance matrix from a limited number of samples. It is of interest to provide criteria to determine if a matrix is bandable, as well as to test the bandedness of a matrix. In this paper, we pose the bandedness testing problem as a hypothesis testing task in statistical signal processing. We then derive two detectors, namely the complex Rao test and the complex Wald test, to test the bandedness of a Cholesky-factor matrix of a covariance matrix’s inverse. Furthermore, in many signal processing fields, such as radar and communications, the covariance matrix and its parameters are often complex-valued; thus, it is of interest to focus on complex-valued cases. The first detector is based on the complex parameter Rao test theorem. It does not require the maximum likelihood estimates of unknown parameters under the alternative hypothesis. We also develop the complex parameter Wald test theorem for general cases and derive the complex Wald test statistic for the bandedness testing problem. Numerical examples and computer simulations are given to evaluate and compare the two detectors’ performance. In addition, we show that the two detectors and the generalized likelihood ratio test are equivalent for the important complex Gaussian linear models and provide an analysis of the root cause of the equivalence.

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Section: Introductionmentioning

confidence: 99%

“…We note that the issue of testing gene-wise independence (e.g. within each tumor type) has drawn increasing attention in the context of testing the sphericity hypothesis, which includes Chen et al, 16 Qiu and Chen, 17 Ledoit and Wolf, 18 Srivastava, 19 Cai et al, 20 Cai and Ma, 21 Peng et al, 22 Ishll et al 23 and Zhang et al 24 However, the issue of data dependence has been considered in Donoho and Jin 25 and Zhong et al 26 for inference about highdimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise dependence. Moreover, Touloumis et al 9 developed a generic and computationally inexpensive nonparametric testing procedure to assess the hypothesis that in each predefined subset of columns (rows), the column (row) mean vector remains constant.…”

Section: Introductionmentioning

confidence: 99%

High-dimensional covariance matrices tests for analyzing multi-tumor gene expression data

Qayed

Han

2021

Stat Methods Med Res

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By collecting multiple sets per subject in microarray data, gene sets analysis requires characterize intra-subject variation using gene expression profiling. For each subject, the data can be written as a matrix with the different subsets of gene expressions (e.g. multiple tumor types) indexing the rows and the genes indexing the columns. To test the assumption of intra-subject (tumor) variation, we present and perform tests of multi-set sphericity and multi-set identity of covariance structures across subjects (tumor types). We demonstrate by both theoretical and empirical studies that the tests have good properties. We applied the proposed tests on The Cancer Genome Atlas (TCGA) and tested covariance structures for the gene expressions across several tumor types.

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More powerful tests for sparse high-dimensional covariances matrices

Cited by 11 publications

References 38 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

Complex Parameter Rao and Wald Tests for Assessing the Bandedness of a Complex-Valued Covariance Matrix

High-dimensional covariance matrices tests for analyzing multi-tumor gene expression data

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