Independent subsets of correlation and other matrices. (English) Zbl 0646.62048

Summary: It is known that the set of correlation coefficients formed from k independent normal samples exhibits pairwise independence of its members [S. Geisser and N. Mantel, Ann. Math. Stat. 33, 290-291 (1962; Zbl 0102.358)]. Here it is shown that many much larger subsets of the matrix are fully independent. The main result characterizes 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.


62H20 Measures of association (correlation, canonical correlation, etc.)
62J15 Paired and multiple comparisons; multiple testing


Zbl 0102.358
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