Marginal and Conditional Multiple Inference for Linear Mixed Model Predictors
针对线性混合模型中集群特定预测量的多重推断问题，提出了一个通用框架，构建了边际和条件法则下的一致性置信集，并发现边际置信集在条件推断中也渐近有效，可用于线性假设检验而无需重抽样。
In spite of its high practical relevance, cluster specific multiple inference for linear mixed model predictors has hardly been addressed so far. While marginal inference for population parameters is well understood, conditional inference for the cluster specific predictors is more intricate. This work introduces a general framework for multiple inference in linear mixed models for cluster specific predictors. Consistent confidence sets for multiple inference are constructed under both, the marginal and the conditional law. Furthermore, it is shown that, remarkably, corresponding multiple marginal confidence sets are also asymptotically valid for conditional inference. Those lend themselves for testing linear hypotheses using standard quantiles without the need of resampling techniques. All findings are validated in simulations and illustrated along a study on Covid-19 mortality in the U.S. state prisons. Supplementary materials for this article are available online.