Title

Weighted Chi-Squared Tests For Partial Common Principal Component Subspaces

Keywords

Correlation matrix; Dimensionality reduction; Principal components analysis

Abstract

We consider tests of the null hypothesis that g covariance matrices have a partial common principal component subspace of dimension s. Our approach uses a dimensionality matrix which has its rank equal to s when the hypothesis holds. The test can then be based on a statistic computed from the eigenvalues of an estimate of this dimensionality matrix. The asymptotic distribution of this statistic is that of a linear combination of independent one-degree-of-freedom chi-squared random variables. Simulation results indicate that this test yields significance levels that come closer to the nominal level than do those of a previously proposed method. The procedure is also extended to a test that g correlation matrices have a partial common principal component subspace.

Publication Date

6-1-2003

Publication Title

Biometrika

Volume

90

Issue

2

Number of Pages

411-421

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1093/biomet/90.2.411

Socpus ID

3843144840 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/3843144840

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