Testing the equality of two high‐dimensional spatial sign covariance matrices

Cheng, Guanghui; Liu, Baisen; Peng, Liuhua; Zhang, Baoxue; Zheng, Shibao

doi:10.1111/sjos.12350

Cited by 9 publications

(3 citation statements)

References 18 publications

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“…The inner products c ij = p −1 tr(Σ i Σ j ) for i = j of the matrix C are also estimated using SSCMs. In this case, however, no error correction due to using the spatial median is needed (see [41]). The estimates for C and ∆ are thus Ĉ = (ĉ ij ) and ∆ = diag( δ1 , .…”

Section: Final Estimatesmentioning

confidence: 99%

Linear Pooling of Sample Covariance Matrices

Raninen

Tyler

Ollila

2022

IEEE Trans. Signal Process.

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We consider the problem of estimating highdimensional covariance matrices of K-populations or classes in the setting where the samples sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a distinct linear combination of all class sample covariance matrices. This approach is shown to reduce the estimation error when the sample sizes are limited, and the true class covariance matrices share a somewhat similar structure. We develop an effective method for estimating the coefficients in the linear combination that minimize the mean squared error under the general assumption that the samples are drawn from (unspecified) elliptically symmetric distributions possessing finite fourth-order moments. To this end, we utilize the spatial sign covariance matrix, which we show (under rather general conditions) to be an unbiased estimator of the normalized covariance matrix as the dimension grows to infinity. We also show how the proposed method can be used in choosing the regularization parameters for multiple target matrices in a single class covariance matrix estimation problem. We assess the proposed method via numerical simulation studies including an application in global minimum variance portfolio optimization using real stock data.

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Section: Final Estimatesmentioning

confidence: 99%

Linear Pooling of Sample Covariance Matrices

Raninen

Tyler

Ollila

2022

IEEE Trans. Signal Process.

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“…Regarding the sphericity, it would be natural to develop an estimator using the SCM as well. However, a simple and particularly well performing estimator of the sphericity is based on the robust spatial sign covariance matrix (SSCM) and it has been used, e.g., in [12], [13], [14], and [11]. Particularly, in [11], both a SCM and a SSCM based estimator of the sphericity was compared and, except for the case where the samples were multivariate normal, the simulations suggested the superiority of the SSCM based estimator for estimating the sphericity.…”

Section: A Our Estimates Of ∆ and Cmentioning

confidence: 99%

Linear pooling of sample covariance matrices

Raninen,

Tyler,

Ollila

2020

Preprint

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We consider covariance matrix estimation in a setting, where there are multiple classes (populations). We propose to estimate each class covariance matrix as a linear combination of all of the class sample covariance matrices. This approach is shown to reduce the estimation error when the sample sizes are limited and the true class covariance matrices share a similar structure. We develop an effective method for estimating the minimum mean squared error coefficients for the linear combination when the samples are drawn from (unspecified) elliptically symmetric distributions with finite fourth-order moments. To this end, we utilize the spatial sign covariance matrix, which we show (under rather general conditions) to be a consistent estimator of the trace normalized covariance matrix as both the sample size and the dimension grow to infinity. We also show how the proposed method can be used in choosing the regularization parameters for multiple target matrices in a single class covariance matrix estimation problem. We assess the proposed method via numerical simulation studies including an application in global minimum variance portfolio optimization using real stock data, where it is shown to outperform several state-of-the-art methods.

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“…The multivariate tests for the homogeneity of HD covariance matrices have received much attention in the past few years. There are many methods designed for comparing two covariances from two independent samples (e.g., Li & Chen, 2012;Yang & Pan, 2017) or several covariances from multiple independent samples (e.g., Schott, 2007;Srivastava & Yanagihara, 2010;Cheng et al, 2019;Zheng et al, 2020). Much of the existing research developed tests under a temporal independence assumption; only Zhong et al (2019) considered HD longitudinal data with 𝑇 fixed and small.…”

Section: Introductionmentioning

confidence: 99%

Homogeneity Tests of Covariance for High-Dimensional Functional Data with Applications to Event Segmentation

Zhong

2023

Biometrics

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We consider inference problems for high‐dimensional (HD) functional data with a dense number of T repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal dependence, high dimensionality, and dense number of repeated measurements pose theoretical and computational challenges. This paper has two aims; our first aim is to solve the theoretical and computational challenges in testing equivalence among covariance matrices from HD functional data. The second aim is to provide computationally efficient and tuning‐free tools with guaranteed stochastic error control. The weak convergence of the stochastic process formed by the test statistics is established under the “large p, large T, and small n” setting. If the null is rejected, we further show that the locations of the change points can be estimated consistently. The estimator's rate of convergence is shown to depend on the data dimension, sample size, number of repeated measurements, and signal‐to‐noise ratio. We also show that our proposed computation algorithms can significantly reduce the computation time and are applicable to real‐world data with a large number of HD‐repeated measurements (e.g., functional magnetic resonance imaging (fMRI) data). Simulation results demonstrate both the finite sample performance and computational effectiveness of our proposed procedures. We observe that the empirical size of the test is well controlled at the nominal level, and the locations of multiple change points can be accurately identified. An application to fMRI data demonstrates that our proposed methods can identify event boundaries in the preface of the television series Sherlock. Code to implement the procedures is available in an R package named TechPhD.

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Testing the equality of two high‐dimensional spatial sign covariance matrices

Cited by 9 publications

References 18 publications

Linear Pooling of Sample Covariance Matrices

Linear Pooling of Sample Covariance Matrices

Linear pooling of sample covariance matrices

Homogeneity Tests of Covariance for High-Dimensional Functional Data with Applications to Event Segmentation

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