Inference and Estimation for Random Effects in High-Dimensional Linear Mixed Models
针对高维线性混合模型，研究了随机效应的假设检验、置信区间和经验贝叶斯估计，并在TIMSS数据上验证了方法有效性。
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.