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

Mervyn J. Silvapulle, Juvêncio S. Nobre, and Julio M. Singer

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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.

Chapter information

N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 197-210

First available in Project Euclid: 1 April 2008

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Mathematical Reviews number (MathSciNet)

Primary: 62F03: Hypothesis testing
Secondary: 62F05: Asymptotic properties of tests

martingales one-sided hypotheses one-way random effects model repeated measures U-statistics variance components

Copyright © 2008, Institute of Mathematical Statistics


Nobre, Juvêncio S.; Singer, Julio M.; Silvapulle, Mervyn J. U -tests for variance components in one-way random effects models. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 197--210, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000149.

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