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Boostrapping Markov Chains
Marko, Dominik ; Prášková, Zuzana (advisor) ; Hušková, Marie (referee)
In this thesis we deal with estimating the transition matrix probabilities of discrete time Markov chains with finite state space. We will use two methods, specifically the maximum likelihood method and the bootstrap method, for obtaining estimators of these matrix probabilities and then we will develop the asymptotic distribution of these estimators. We will describe the basic characteristics of the bootstrap method and show the application of two bootstrap methods used for estimating transition probabilites, specifically conditional bootstrap and standard bootstrap. The results of the application of every method used for obtaining transition probabilities and computing confidence intervals will be presented in a numerical study and compared with the results based on asymptotic normality. Powered by TCPDF (www.tcpdf.org)
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Truncated data and stochastic claims reserving
Marko, Dominik ; Pešta, Michal (advisor) ; Mazurová, Lucie (referee)
In this thesis stochastic claims reserving under the model of randomly trun- cated data is presented. For modelling the claims, a compound Poisson process is assumed. Introducing a random variable representing the delay between oc- currence and reporting of a claim, a probability model of IBNR claims is built. The fact that some claims are incurred but not reported yet leads to truncated data. Basic results of non-parametric statistical estimation under the model of randomly truncated data are shown, which can be used to obtain an estimate of IBNR claims reserves. Theoretical background is then used for application on real data from Czech Insurers' Bureau. 36
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Boostrapping Markov Chains
Marko, Dominik ; Prášková, Zuzana (advisor) ; Hušková, Marie (referee)
In this thesis we deal with estimating the transition matrix probabilities of discrete time Markov chains with finite state space. We will use two methods, specifically the maximum likelihood method and the bootstrap method, for obtaining estimators of these matrix probabilities and then we will develop the asymptotic distribution of these estimators. We will describe the basic characteristics of the bootstrap method and show the application of two bootstrap methods used for estimating transition probabilites, specifically conditional bootstrap and standard bootstrap. The results of the application of every method used for obtaining transition probabilities and computing confidence intervals will be presented in a numerical study and compared with the results based on asymptotic normality. Powered by TCPDF (www.tcpdf.org)
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