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December, 1983 A Class of Asymptotic Tests for Principal Component Vectors
David E. Tyler
Ann. Statist. 11(4): 1243-1250 (December, 1983). DOI: 10.1214/aos/1176346337


In this paper, the hypothesis that a set of vectors lie in the subspace spanned by a prescribed subset of the principal component vectors for a normal population is considered. A class of invariant asymptotic tests based on the sample covariance matrix is derived. Tests in this class are shown to be consistent and their local power functions are given. The arguments used in deriving the class of tests are not heavily dependent on the assumption of normality nor on the use of the sample covariance matrix. The results are shown to generalize when the procedures are based on any affine-invariant $M$-estimate of scatter and when the population is elliptical.


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David E. Tyler. "A Class of Asymptotic Tests for Principal Component Vectors." Ann. Statist. 11 (4) 1243 - 1250, December, 1983.


Published: December, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0544.62053
MathSciNet: MR720269
Digital Object Identifier: 10.1214/aos/1176346337

Primary: 62H15
Secondary: 62E20, 62H20, 62H25

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 4 • December, 1983
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