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June, 1986 Asymptotic Theory for Common Principal Component Analysis
Bernard N. Flury
Ann. Statist. 14(2): 418-430 (June, 1986). DOI: 10.1214/aos/1176349930

Abstract

Under the common principal component model $k$ covariance matrices $\mathbf{\Sigma}_1,\cdots,\mathbf{\Sigma}_k$ are simultaneously diagonalizable, i.e., there exists an orthogonal matrix $\mathbf{\beta}$ such that $\mathbf{\beta'\Sigma_i\beta = \Lambda_i}$ is diagonal for $i = 1,\cdots, k$. In this article we give the asymptotic distribution of the maximum likelihood estimates of $\mathbf{\beta}$ and $\mathbf{\Lambda}_i$. Using these results, we derive tests for (a) equality of eigenvectors with a given set of orthonormal vectors, and (b) redundancy of $p - q$ (out of $p$) principal components. The likelihood-ratio test for simultaneous sphericity of $p - q$ principal components in $k$ populations is derived, and some of the results are illustrated by a biometrical example.

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Bernard N. Flury. "Asymptotic Theory for Common Principal Component Analysis." Ann. Statist. 14 (2) 418 - 430, June, 1986. https://doi.org/10.1214/aos/1176349930

Information

Published: June, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0613.62075
MathSciNet: MR840506
Digital Object Identifier: 10.1214/aos/1176349930

Subjects:
Primary: 62H25
Secondary: 62E20, 62H15

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 2 • June, 1986
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