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The COVID-19 pandemic has had far-reaching consequences, highlighting the urgency for explanatory and predictive tools to track infection rates and burden of care over time and space. However, the scarcity and inhomogeneity of data is a challenge. In this research we develop a robust framework for estimating and predicting the occupied beds of Intensive Care Units by presenting an innovative Small Area Estimation methodology based on the definition of mixed models with random regression coefficients. We applied it to estimate and predict the daily occupancy of Intensive Care Unit beds by COVID-19 in health areas of Castilla y Le\'on, from November 2020 to March 2022., Comment: Main: 21 pages, 10 figures and 2 tables. Supplementary material: 16 pages, 10 figures and 4 tables

Today, generalized linear mixed models are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under generalized linear mixed models. In addition, we implement our methodology to study widely employed examples of mixed models, that is, the unit-level binomial, the area-level Poisson-gamma and the area-level Poisson-lognormal mixed models. The asymptotic results are accompanied by extensive simulations. A case study on predicting poverty rates illustrates applicability and advantages of our simultaneous inference tools., Comment: 46 pages, 20 figures; simulations and data analysis expanded, additional remarks added

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., Comment: 36 pages, 6 figures, a new version includes additional simulation results, a modified data analysis and some changes in the notation