# On a likelihood ratio test for independence

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## Abstract

The likelihood-ratio (LR) statistic is derived for testing the hypothesis of independence between k subvectors of a normally distributed random vector X against the alternative that exactly s, 2 [less-than-or-equals, slant] s [less-than-or-equals, slant] k, subvectors are dependent. A null asymptotic distribution for the LR statistic is also presented.

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