Projection tests for high-dimensional spiked covariance matrices
type: Item
instance of: scholarly article
title: Projection tests for high-dimensional spiked covariance matrices
zbMATH Open document ID: 1411.62149
published in: Journal of Multivariate Analysis
publication date: 2019-01-04T00:00:00Z
review text: Let \(X_1,X_2,\ldots, X_n\) be independent and identically distributed \(p\)-dimensional random vectors with covariance matrix \(\Sigma=\mathbb{I}_p+\mathbb{V}\Omega \mathbb{V}^{T}\), where \(\mathbb{I}_p\) is the \(p\)-dimensional identity matrix, \(\Omega=\text{diag}(\omega_1,\ldots,\omega_K)\) with \(\omega_1\geq\ldots\geq\omega_K>0\), and \(\mathbb{V}\) is a \(p\times K\) matrix with orthogonal and unit columns. The authors of the paper consider problems related to the testing of the following hypotheses: \[ \begin{aligned} & \Big\{\mathcal{H}_0:\Sigma=\mathbb{I}_p \;\text{vs.}\;\mathcal{H}_1 : \Sigma=\mathbb{I}_p+\mathbb{V}\Omega \mathbb{V}^{T}\Big\},\\ & \Big\{\mathcal{H}_0:\Sigma=\sigma^2\mathbb{I}_p \;\text{vs.}\;\mathcal{H}_1 : \Sigma=\sigma^2(\mathbb{I}_p+\mathbb{V}\Omega \mathbb{V}^{T})\Big\}, \end{aligned} \] where \(\sigma^2\) is an unknown but finite positive constant. New tests based on a projection approach are developed for the high-dimensional case. The asymptotic distribution of the proposed tests are obtained under suitable regularity conditions.
reviewed by: Jonas Šiaulys
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 62H25
zbMATH DE Number: 6997742
zbMATH Keywords: large \(p\) small \(n\)
zbMATH Keywords: power enhancement technique
zbMATH Keywords: projection
zbMATH Keywords: spiked covariance matrix
author: WenWen Guo
author: Hengjian Cui
MaRDI profile type: Publication
full work available at URL: j.jmva.2018.08.009
OpenAlex ID: W2889348644
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Wikidata QID: Q129336306
DOI: 10.1016/J.JMVA.2018.08.009
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description: scientific article; zbMATH DE number 6997742