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U-tests for variance components in linear mixed models

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  • Juvêncio Nobre
  • Julio Singer
  • Pranab Sen

Abstract

We propose a U-statistics-based test for null variance components in linear mixed models and obtain its asymptotic distribution (for increasing number of units) under mild regularity conditions that include only the existence of the second moment for the random effects and of the fourth moment for the conditional errors. We employ contiguity arguments to derive the distribution of the test under local alternatives assuming additionally the existence of the fourth moment of the random effects. Our proposal is easy to implement and may be applied to a wide class of linear mixed models. We also consider a simulation study to evaluate the behaviour of the U-test in small and moderate samples and compare its performance with that of exact F-tests and of generalized likelihood ratio tests obtained under the assumption of normality. A practical example in which the normality assumption is not reasonable is included as illustration. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Juvêncio Nobre & Julio Singer & Pranab Sen, 2013. "U-tests for variance components in linear mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 580-605, November.
    • Handle: RePEc:spr:testjl:v:22:y:2013:i:4:p:580-605
    DOI: 10.1007/s11749-013-0316-8
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    References listed on IDEAS

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    3. Li, Zaixing, 2015. "A residual-based test for variance components in linear mixed models," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 73-78.
    4. Zaixing Li, 2017. "Inference of nonlinear mixed models for clustered data under moment conditions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 759-781, December.
    5. Artur Lemonte, 2015. "On local power properties of the LR, Wald, score and gradient tests in nonlinear mixed-effects models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 885-895, October.

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