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Truncated random vectors
Raab, Petr ; Pešta, Michal (advisor) ; Komárek, Arnošt (referee)
This bachelor thesis deals with truncated random vectors, distributions and properties of theirs. Truncated random vectors theory is then used to solve problem of delayed reporting of non-life insurance claims. At the of this thesis there are shown properties and behaviour of the estimators, which are constructed in this thesis, while being applicated on real life data from vehicle accident insurancy. 1
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Cox model with interval-censored data
Štarmanová, Petra ; Komárek, Arnošt (advisor) ; Hlubinka, Daniel (referee)
Survival analysis typically deals with censored data. This thesis focuses on interval- censored data, which are common in medical studies. We present regression models for analysing interval-censored data with emphasis on semiparametric models. We study the models of Finkelstein and Farrington in depth and show their use on real data. The properties of both models are explored in a simulation study. 1
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Errors in Variables
Mordinová, Katarína ; Hlávka, Zdeněk (advisor) ; Komárek, Arnošt (referee)
1 Title: Errors in variables Author: Katarína Mordinová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Zdeněk Hlávka, Ph.D. Supervisor's e-mail address: Zdenek.Hlavka@mff.cuni.cz Abstract: The topic of the diploma thesis is Errors in variables. In the opening chapter, we define basic terms used in the thesis and we introduce the regression analysis and basic relations related to this term. In the second chapter, we attend to linear regression model and its characteristics. In the third chapter, we attend to the errors in variables models. In the last chapter of this thesis we present a possible application in medicine. Keywords: regresion analysis, errors in variables, linear regression model
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Dynamic model for estimation of radon concentration in buildings
Vaňková, Barbora ; Brabec, Marek (advisor) ; Komárek, Arnošt (referee)
Title: Dynamic model for estimation of radon concentration in buildings Author: Barbora Vaňková Department: Department of probability and mathematical statistics Supervisor: Ing. Marek Brabec, Ph.D. Supervisor's e-mail address: mbrabec@cs.cas.cz Abstract: In the present work there is described the method for estimation of functi- onal data from discrete values and basic methods of functional data analysis. 1
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Group sequential tests in clinical trials
Jílek, Josef ; Kulich, Michal (advisor) ; Komárek, Arnošt (referee)
Group sequential tests are an important statistical method. The analysis of data are performed continuously, which allows us to terminate the test before all observations are collected. For example these tests are used in medicine. When testing new drugs or procedures, this method brings about financial savings as well as ethical advantages. There are many ways of conducting group sequential tests with different qualities. Based on the perused literature, both basic and more complex types of group sequential tests are introduced in this paper. It discribes their principle and respective examples are provided. With this information it is possible to design and conduct a particular test. It's merits and demerits are compared for every method in real situations. The result is a tabular scale of different tests, from which it is possible to select a particular test for a given situation.
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Regression models with alternatively distributed response
Kučera, Tomáš ; Komárek, Arnošt (advisor) ; Zvára, Karel (referee)
This thesis deals with regression models in the case of binary response variable. Linear and logistic regression models are defined for different types of predictors. Then the thesis uses the theory of maximum likelihood and applies it to the special case of logistic regression model. Both exact inference of model parameters and hypothesis testing with related interval inference are discussed. Suitable methods for numerical solving of selected methods are suggested. In the final part, the discussed methods are applied to real credit scoring data from the field of banking, using the statistical software R.
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Odhad momentů při intervalovém cenzorování typu I
Ďurčík, Matej ; Komárek, Arnošt (advisor) ; Kulich, Michal (referee)
Title: Moments Estimation under Type I Interval Censoring Author: Matej Ďurčík Department: Faculty of Probability and Mathematical Statistics Supervisor: RNDr. Arnošt Komárek Ph.D. Abstract: In this thesis we apply the uniform deconvolution model to the interval censoring problem. We restrict ourselves only on interval censoring case 1. We show how to apply uniform deconvolution model in estimating the probability distribution characteristics in the interval censoring case 1. Moreover we derive limit distributions of the estimators of mean and variance. Then we compare these estimators to the asymptotically efficient estimators based on the nonparametric maximum likelihood estimation by simulation studies under some certain distributions of the random variables. 1
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Computational Methods for Maximum Likelihood Estimation in Generalized Linear Mixed Models
Otava, Martin ; Komárek, Arnošt (advisor) ; Kulich, Michal (referee)
of the diploma thesis Title: Computational Methods for Maximum Likelihood Estimation in Generalized Linear Mixed Models Author: Bc. Martin Otava Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Arnošt Komárek, Ph.D., Department of Probability and Mathematical Statistics Abstract: Using maximum likelihood method for generalized linear mixed models, the analytically unsolvable problem of maximization can occur. As solution, iterative and ap- proximate methods are used. The latter ones are core of the thesis. Detailed and general introducing of the widely used methods is emphasized with algorithms useful in practical cases. Also the case of non-gaussian random effects is discussed. The approximate methods are demonstrated using the real data sets. Conclusions about bias and consistency are supported by the simulation study. Keywords: generalized linear mixed model, penalized quasi-likelihood, adaptive Gauss- Hermite quadrature 1
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Parameter estimation in case-cohort studies
Klášterecký, Petr ; Kulich, Michal (advisor) ; Volf, Petr (referee) ; Komárek, Arnošt (referee)
The concern of this thesis is parameter estimation in regression models in survival analysis, particularly in case-cohort studies. In case-cohort studies, observations are sampled to form a subcohort which is followed and analysed. As a result, the cost of performing such studies is reduced but standard procedures for parameter estimation need to be modified. This is usually done by incorporating weights into the estimating equations so that individual sampling probabilities are accounted for. In this thesis we show that this method can lead to biased estimators when the subcohort sampling probability is low and suggest an alternative estimator based on logistic regression.
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