Simultaneous inference for linear mixed model parameters with an application to small area estimation
针对线性混合模型中混合参数的联合推断问题，提出了联合预测区间和多重检验方法，通过自助法近似最大型统计量的分布，并在小区域家庭收入数据中验证了方法有效性。
Summary Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical tools for valid simultaneous inference for mixed parameters are rare. This is surprising because one often faces inferential problems beyond the pointwise examination of fixed or mixed parameters. For example, there is an interest in a comparative analysis of cluster‐level parameters or subject‐specific estimates in studies with repeated measurements. We discuss methods for simultaneous inference assuming a linear mixed model. Specifically, we develop simultaneous prediction intervals as well as multiple testing procedures for mixed parameters. They are useful for joint considerations or comparisons of cluster‐level parameters. We employ a consistent bootstrap approximation of the distribution of max‐type statistic to construct our tools. The numerical performance of the developed methodology is studied in simulation experiments and illustrated in a data example on household incomes in small areas.