The Annals of Mathematical Statistics

The Distribution of the Latent Roots of the Covariance Matrix

Alan T. James

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Abstract

The distribution of the latent roots of the covariance matrix calculated from a sample from a normal multivariate population, was found by Fisher [3], Hsu [6] and Roy [10] for the special, but important case when the population covariance matrix is a scalar matrix, $\Sigma = \sigma^2I$. By use of the representation theory of the linear group, we are able to obtain the general distribution for arbitrary $\Sigma$.

Article information

Source
Ann. Math. Statist. Volume 31, Number 1 (1960), 151-158.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177705994

Digital Object Identifier
doi:10.1214/aoms/1177705994

Mathematical Reviews number (MathSciNet)
MR126901

Zentralblatt MATH identifier
0201.52401

JSTOR
links.jstor.org

Citation

James, Alan T. The Distribution of the Latent Roots of the Covariance Matrix. Ann. Math. Statist. 31 (1960), no. 1, 151--158. doi:10.1214/aoms/1177705994. https://projecteuclid.org/euclid.aoms/1177705994


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