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Permutation Tests for Linear Models

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Several approximate permutation tests have been proposed for tests of partial regression coefficients in a linear model based on sample partial correlations. This paper begins with an explanation and notation for an exact test. It then compares the distributions of the test statistics under the various permutation methods proposed, and shows that the partial correlations under permutation are asymptotically jointly normal with means 0 and variances 1. The method of Freedman & Lane (1983) is found to have asymptotic correlation 1 with the exact test, and the other methods are found to have smaller correlations with this test. Under local alternatives the critical values of all the approximate permutation tests converge to the same constant, so they all have the same asymptotic power. Simulations demonstrate these theoretical results.
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Keywords: asymptotics; partial correlations; power; resampling

Document Type: Research Article

Affiliations: 1: Centre for Research on Ecological Impacts of Coastal Cities, University of Sydney, Australia, 2: School of Mathematics and Statistics, University of Sydney, Australia

Publication date: March 1, 2001

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