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Inference for mixed models of ANOVA type with high-dimensional data

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Listed:
  • Chen, Fei
  • Li, Zaixing
  • Shi, Lei
  • Zhu, Lixing

Abstract

Inference for variance components in linear mixed models of ANOVA type, including estimation and testing, has been investigated when the number of fixed effects is fixed. However, for high-dimensional data, this number is large and would be regarded as a divergent value as the sample size goes to infinity. In this paper, existing tests are extended to handle this problem with a sparse model structure. To avoid the impact from insignificant fixed effects, the proposed tests are post-selection-based with an orthogonality-based selection of SCAD type applied to selecting significant fixed effects into working model. The selection and estimation of fixed effects are under the assumption on the existence of second order moments for errors. Two types of tests for random effects are considered and some new insights are obtained. The proposed tests are distribution-free, though they request the existence of the fourth moments of random effects and errors. The proposed methods are illustrated by simulation studies and a real data analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:382-401
    DOI: 10.1016/j.jmva.2014.09.013
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    6. 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.
    7. Pinheiro, Aluísio & Sen, Pranab Kumar & Pinheiro, Hildete Prisco, 2009. "Decomposability of high-dimensional diversity measures: Quasi-U-statistics, martingales and nonstandard asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1645-1656, September.
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    1. Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.

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