The Annals of Mathematical Statistics

On the Distribution of Sums of Squares and Cross Products of Normal Variates in the Presence of Intra-class Correlation

Donald F. Morrison

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Abstract

The sums of squares and cross products of groups of random variables drawn from a multivariate normal population whose covariance matrix has a certain pattern indicating intra-class correlations are shown to follow the Wishart distribution. It follows immediately from this result that the usual distributions of the simple, partial, and multiple correlation coefficients obtain, although with non-centrality parameters that reflect the effect of the intra-class correlations.

Article information

Source
Ann. Math. Statist., Volume 33, Number 4 (1962), 1461-1463.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177704379

Digital Object Identifier
doi:10.1214/aoms/1177704379

Mathematical Reviews number (MathSciNet)
MR142173

Zentralblatt MATH identifier
0124.11301

JSTOR
links.jstor.org

Citation

Morrison, Donald F. On the Distribution of Sums of Squares and Cross Products of Normal Variates in the Presence of Intra-class Correlation. Ann. Math. Statist. 33 (1962), no. 4, 1461--1463. doi:10.1214/aoms/1177704379. https://projecteuclid.org/euclid.aoms/1177704379


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