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Variance Components Testing in ANOVA-Type Mixed Models

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  • Zaixing Li
  • Fei Chen
  • Lixing Zhu

Abstract

type="main" xml:id="sjos12044-abs-0001"> The purpose of this article is threefold. First, variance components testing for ANOVA-type mixed models is considered, in which response may not be divided into independent sub-vectors, whereas most of existing methods are for models where response can be divided into independent sub-vectors. Second, testing that a certain subset of variance components is zero. Third, as normality is often violated in practice, it is desirable to construct tests under very mild assumptions. To achieve these goals, an adaptive difference-based test and an adaptive trace-based test are constructed. The test statistics are asymptotically normal under the null hypothesis, are consistent against all global alternatives and can detect local alternatives distinct from the null at a rate as close to n-super- − 1 ∕ 2 as possible with n being the sample size. Moreover, when the dimensions of variance components in different sets are bounded, we develop a test with chi-square as its limiting null distribution. The finite sample performance of the tests is examined via simulations, and a real data set is analysed for illustration.

Suggested Citation

  • Zaixing Li & Fei Chen & Lixing Zhu, 2014. "Variance Components Testing in ANOVA-Type Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 482-496, June.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:482-496
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    References listed on IDEAS

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    1. Zaixing Li & Lixing Zhu, 2010. "On Variance Components in Semiparametric Mixed Models for Longitudinal Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 442-457, September.
    2. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    3. Cibele Russo & Reiko Aoki & Gilberto Paula, 2012. "Assessment of variance components in nonlinear mixed-effects elliptical models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 519-545, September.
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    1. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    2. Chen, Fei & Li, Zaixing & Shi, Lei & Zhu, Lixing, 2015. "Inference for mixed models of ANOVA type with high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 382-401.
    3. 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.
    4. Li, Zaixing, 2015. "A residual-based test for variance components in linear mixed models," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 73-78.
    5. Zaixing Li & Fei Chen & Lixing Zhu, 2017. "Estimating moments in ANOVA-type mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 697-715, November.
    6. Imori, Shinpei & Rosen, Dietrich von, 2015. "Covariance components selection in high-dimensional growth curve model with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 86-94.

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