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Inference and Estimation for Random Effects in High-Dimensional Linear Mixed Models

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  • Michael Law
  • Ya’acov Ritov

Abstract

We consider three problems in high-dimensional linear mixed models. Without any assumptions on the design for the fixed effects, we construct asymptotic statistics for testing whether a collection of random effects is zero, derive an asymptotic confidence interval for a single random effect at the parametric rate n , and propose an empirical Bayes estimator for a part of the mean vector in ANOVA type models that performs asymptotically as well as the oracle Bayes estimator. We support our theoretical results with numerical simulations and provide comparisons with oracle estimators. The procedures developed are applied to the Trends in International Mathematics and Sciences Study (TIMSS) data. Supplementary materials for this article are available online.

Suggested Citation

  • Michael Law & Ya’acov Ritov, 2023. "Inference and Estimation for Random Effects in High-Dimensional Linear Mixed Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1682-1691, July.
    • Handle: RePEc:taf:jnlasa:v:118:y:2023:i:543:p:1682-1691
    DOI: 10.1080/01621459.2021.2004896
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