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

Fei Chen, Zaixing Li, Lei Shi, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)382-401
Number of pages20
JournalJournal of Multivariate Analysis
Volume133
DOIs
Publication statusPublished - 1 Jan 2015

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • 62H15
  • Fixed effect selection
  • Linear mixed model
  • Shrinkage estimation
  • Test for variance components

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