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

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dc.creatorNobre, Juvêncio S.
dc.creatorSinger, Julio M.
dc.creatorSilvapulle, Mervyn J.
dc.date2008-05-15
dc.date.accessioned2026-07-07T12:18:56Z
dc.date.available2026-07-07T12:18:56Z
dc.descriptionWe 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/193940307000000149 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0805.2316
dc.identifierhttp://arxiv.org/abs/0805.2316
dc.identifierIMS Collections 2008, Vol. 1, 197-210
dc.identifierdoi:10.1214/193940307000000149
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212583
dc.subjectStatistics Theory
dc.subject62F03 (Primary) 62F05 (Secondary)
dc.title$U$-tests for variance components in one-way random effects models
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