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December, 1983 The Asymptotic Distribution of Principal Component Roots Under Local Alternatives to Multiple Roots
David E. Tyler
Ann. Statist. 11(4): 1232-1242 (December, 1983). DOI: 10.1214/aos/1176346336

Abstract

The asymptotic distribution for the principal component roots under local alternatives to multiple population roots is derived. The asymptotic theory assumes the estimate of the population covariance or scatter matrix to be asymptotically normal and to possess certain invariance properties. These assumptions are satisfied for the affine-invariant $M$-estimates of scatter for an elliptical distribution. The local alternative framework is used in deriving a local power function for the test for subsphericity.

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David E. Tyler. "The Asymptotic Distribution of Principal Component Roots Under Local Alternatives to Multiple Roots." Ann. Statist. 11 (4) 1232 - 1242, December, 1983. https://doi.org/10.1214/aos/1176346336

Information

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

zbMATH: 0546.62007
MathSciNet: MR720268
Digital Object Identifier: 10.1214/aos/1176346336

Subjects:
Primary: 62E20
Secondary: 62H10, 62H25

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 4 • December, 1983
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