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Generalized estimating equaitons
Sotáková, Martina ; Omelka, Marek (advisor) ; Antoch, Jaromír (referee)
In this thesis we are interested in generalized estimating equations (GEE). First, we introduce the term of generalized linear model, on which generalized estimating equations are based. Next we present the methos of pseudo maximum likelyhood and quasi-pseudo maximum likelyhood, from which we move on to the methods of generalized estimating equations. Finally, we perform simulation studies, which demonstrates the theoretical results presented in the thesis. 1
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Claims reserving within the panel data framework
Gerthofer, Michal ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
In the presented thesis the issue of dependency between response variables within the subjects in the generalized linear models framework is investigated. Reserving in non-life insurance is a key factor for the financial position of a company. The text introduces the basic actuarial notation, terminology and methods. The main part is focused on panel data framework, especially Generalized Linear Mixed Models (GLMM) as well as Generalized Estimating Equations (GEE), and their application on claims reserving. The aim of this thesis is to show the advantages, disadvantages, limitations and the comparison of these approaches on representative datasets, which were chosen according to results obtained from whole database analysis. Significant focus is on model selection and diagnostics used for this purpose. Finally, the obtained results are summarized in tables, figures and the comparison of the methods is provided. Powered by TCPDF (www.tcpdf.org)
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Modeling dependencies in claims reserving
Kaderjáková, Zuzana ; Pešta, Michal (advisor) ; Branda, Martin (referee)
The generalized linear models (GLM) lately received a lot of attention in modelling the insurance data. However, the violation of assumptions about the independence of underlying data set often causes problems and misinterpretation of achieved results. The need for more exible instruments has been spoken out and consequently various proposals have been made. This thesis deals with GLM based techniques enabling to handle correlated data sets. The usage have been made of generalized linear mixed models (GLMM) and generalized estimating equations (GEE). The main aim of this thesis is to provide a solid statistical background and perform a practical application to demonstrate and compare features of various models. Powered by TCPDF (www.tcpdf.org)
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