  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.
