Simultaneous and post-selection inference for mixed parameters

Diplôme Thèse Simultaneous and post-selection inference for mixed parameters eng 2020-07-03 author Reluga Katarzyna 861310 director Sperlich Stefan Andréas 729471 director Lombardía María-José 10.13097/archive-ouverte/unige:138615 urn:nbn:ch:unige-1386154 GSEM 81 This thesis primarily focuses on the development of statistically valid tools for simultaneous and post-selection inference for a mixed parameter under linear mixed models (LMM) and generalised LMM (GLMM) as well as the investigation of their performance in practice. First, we construct simultaneous confidence intervals for mixed parameters using the max-type statistic, which is readily applicable in the multiple testing procedure. We show that the cluster-wise inference is statistically invalid once we deal with joint statements and it may lead to completely erroneous conclusions. Second, we deal with the simultaneous inference for empirical best predictors in GLMM. Finally, we investigate the issue of post-selection inference for a mixed parameter using conditional Akaike information criterion as a model selection procedure. Within the framework of LMM, we develop a complete theory to construct confidence intervals for mixed parameters under three frameworks: nested and general models, as well as a misspecified setting. Area-level model Conditional Akaike information criterion Empirical best predictor Generalised linear mixed model Linear mixed models Max-type statistic Mixed parameter Multiple testing Post-selection inference Simultaneous confidence intervals Small area estimation Unit-level model Dewey 310 117 Research Center for Statistics S5 false e1e4fed8-eb00-4f31-8e1f-bb02fcac01e2 Thesis Public Reluga_PhD_Thesis.pdf 7127246 application/pdf Restricted 2021-07-27 f0b2a18e95a7accbd8c6ae4e4b63b8f82857c37ec71718bd37261485c75e02df openAccess Faculté d'économie et de management / Research Center for Statistics

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Reluga, Katarzyna