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Improved \(U\)-tests for variance components in one-way random effects models. (English) Zbl 1445.62120
Summary: Based on a decomposition of a \(U\)-statistic, N. Balakrishnan (ed.) et al. [Beyond parametrics in interdisciplinary research: Festschrift in honor of Professor Pranab K. Sen. Beachwood, OH: IMS, Institute of Mathematical Statistics (2008; Zbl 1159.62002)] proposed a test for the hypothesis that the within-treatment variance component in a one-way random effects model is null, specially useful when very mild assumptions are imposed on the underlying distributions. We consider a bootstrap version of that \(U\)-test and evaluate its performance via simulation studies in different scenarios. The bootstrap \(U\)-test has better statistical properties than the original test even in small samples. Furthermore, it is easy to implement and has a low computational cost. We consider two examples with unbalanced small sample datasets, for illustrative purposes.
MSC:
62H15 Hypothesis testing in multivariate analysis
62G30 Order statistics; empirical distribution functions
62P10 Applications of statistics to biology and medical sciences; meta analysis
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