
Modeling transition intensities of a nonhomogenous Markov chain via the Cox model
Jandl, Vojtěch ; Kulich, Michal (advisor) ; Komárek, Arnošt (referee)
We study the extension of methods from the classical twostate survival analysis to the multistate setting. Such models are applicable in a variety of fields in situations, for which the classical case does not suffice due to the fact that omission of some states is not possible. First of all, we explore one sample methods, in particular the extensions of the well known NelsonAalen and KaplanMeier estimators. Then, we deal with regression models for transition intensities, which include a generalisation of the Cox model, and the LinYing additive model, for which we derive the asymptotic properties of the estimator of regression parameters. Lastly, to illustrate the practicality of presented methods, we propose an experiment that could help a website understand the behaviour of its members. A small simulation study is also a part of the last chapter in order to demonstrate the asymptotic properties of the underlying model empirically. 1


Classification based on mixture models
Janečková, Lucie ; Komárek, Arnošt (advisor) ; Maciak, Matúš (referee)
This thesis deals with classification based on mixture models, mainly on models finite normal. At first, there are introduced basic definitions and characteristics of finite mix tures. Afterwards there is described the maximum likelihood method and her obstacles in context of finite mixtures, which we are using for unknown parameters estimation. Then there is described EM algorithm, that is used to obtain the maximum likelihood estimator and there are calculated the formulae for one iteration of EM algorithm. In the last part there is shown, how can finite normal mixtures be used for classification. 1


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 nonlife 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


Cox model with intervalcensored 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 intervalcensored 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


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 email 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


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 email 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


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.

 

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.


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
