The Annals of Mathematical Statistics

On the Distribution of a Multiple Correlation Matrix: Non-Central Multivariate Beta Distributions

M. S. Srivastava

Full-text: Open access

Abstract

Of several possible versions of multiple correlation matrix between two sets of variables $\mathbf{x}$ and $\mathbf{y}$ (see, e.g., Khatri, 1964), we derive using the techniques of A. T. James (zonal polynomials), the non-null distribution of one version when (i) one of the two sets of variables is fixed, i.e., multivariate analysis of variance and covariance case (MANOVA), and when (ii) both sets of variables are random variables, i.e., canonical correlations case. These distributions are non-central multivariate $\beta$-distributions in much the same way as the two cases of multiple correlation commonly known as the multiple correlation of the second and the first kind respectively.

Article information

Source
Ann. Math. Statist., Volume 39, Number 1 (1968), 227-232.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177698522

Digital Object Identifier
doi:10.1214/aoms/1177698522

Mathematical Reviews number (MathSciNet)
MR219186

Zentralblatt MATH identifier
0174.22905

JSTOR
links.jstor.org

Citation

Srivastava, M. S. On the Distribution of a Multiple Correlation Matrix: Non-Central Multivariate Beta Distributions. Ann. Math. Statist. 39 (1968), no. 1, 227--232. doi:10.1214/aoms/1177698522. https://projecteuclid.org/euclid.aoms/1177698522


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Corrections

  • See Correction: M. S. Srivastava. Correction Notes: Correction to "On the Distribution of a Multiple Correlation Matrix: Non-Central Multivariate Beta-Distributions". Ann. Math. Statist., Volume 39, Number 4 (1968), 1359--1359.