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A Simple Test For The Independence of Sets of Variables
Author(s) -
Maritz A.
Publication year - 1981
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1981.tb00760.x
Subject(s) - mathematics , independence (probability theory) , likelihood ratio test , statistic , statistics , test (biology) , diagonal , test statistic , simple (philosophy) , statistical hypothesis testing , geometry , paleontology , philosophy , epistemology , biology
Summary A test for the mutual independence of subvectors of the p ‐dimensional random vector X , distributed as N ( 0, S̀ ), is described. The test is based on the maximum likelihood estimates (MLEs) of the off‐(block) diagonal elements of S̀. It is shown that the resulting test statistic is much easier to compute than the likelihood ratio (LR) test statistic while retaining the same asymptotic power properties in view of the general properties of tests based on the MLEs (ML test) and the likelihood ratio (LR test).