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

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...