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January, 1987 Independent Subsets of Correlation and Other Matrices
Timothy C. Brown
Ann. Probab. 15(1): 416-422 (January, 1987). DOI: 10.1214/aop/1176992279


It is known that the set of correlation coefficients formed from $k$ independent normal samples exhibits pairwise independence of its members (Geisser and Mantel (1962)). Here it is shown that many much larger subsets of the matrix are fully independent. The main result characterises such subsets in a simple way. Because the results are framed in abstract terms, they also apply to rank correlation coefficients and $\chi^2$ statistics.


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Timothy C. Brown. "Independent Subsets of Correlation and Other Matrices." Ann. Probab. 15 (1) 416 - 422, January, 1987.


Published: January, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0646.62048
MathSciNet: MR877613
Digital Object Identifier: 10.1214/aop/1176992279

Primary: 62J15
Secondary: 60E99 , 60G55

Keywords: $\chi^2$ statistics , Correlation matrix , distances on metric space , partial independence , uniform distribution

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 1 • January, 1987
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