$U$-tests for variance components in one-way random effects models

Details $U$-tests for variance components in one-way random effects models $U$-tests for variance components in one-way random effects models

2008-05-15

arxiv.org/abs/0805.2316v1

IMS Collections 2008, Vol. 1, 197-210

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/193940307000000149 the IMS Collections (http://www.imstat.org/publications/imscollec

Scientific paper

10.1214/193940307000000149

We consider a test for the hypothesis that the within-treatment variance component in a one-way random effects model is null. This test is based on a decomposition of a $U$-statistic. Its asymptotic null distribution is derived under the mild regularity condition that the second moment of the random effects and the fourth moment of the within-treatment errors are finite. Under the additional assumption that the fourth moment of the random effect is finite, we also derive the distribution of the proposed $U$-test statistic under a sequence of local alternative hypotheses. We report the results of a simulation study conducted to compare the performance of the $U$-test with that of the usual $F$-test. The main conclusions of the simulation study are that (i) under normality or under moderate degrees of imbalance in the design, the $F$-test behaves well when compared to the $U$-test, and (ii) when the distribution of the random effects and within-treatment errors are nonnormal, the $U$-test is preferable even when the number of treatments is small.

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