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Title: Simultaneous inference for empirical the best predictor under generalized linear mixed models Authors:  Katarzyna Reluga - University of Geneva (Switzerland) [presenting]
Maria Jose Lombardia - Universidade da Coruna (Spain)
Stefan Sperlich - University of Geneva (Switzerland)
Abstract: Simultaneous inference is considered for the empirical best predictor under generalized linear mixed models. In particular, we propose a method to construct simultaneous prediction intervals (SPIs). To the best of our knowledge, SPIs have not been developed under this modelling framework. SPIs allow researchers and practitioners to carry out statistically valid multiple comparisons of all or several parameters of interest. Aforementioned analysis can be desirable within certain domains such as small area estimation, which is often applied in, among others, studies measuring poverty, policy-making or ecological and demographic projects. Moreover, we develop a multiple testing procedure employing a max-type statistic. We focus on the maximum likelihood based estimation. We provide some details regarding the area-level Poisson model. A proof of the asymptotic coverage probability of simultaneous bands is provided. The theoretical results are accompanied by an extensive simulation experiment and a data example. The latter reveals an advantage of SPIs in the simultaneous study of the estimators. On the other hand, in this situation, the cluster-wise confidence intervals do not account for the variability arising from the joint statements and may lead to completely erroneous conclusions.