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Tests of independence in contingency tables
Pavlík, Lukáš ; Maciak, Matúš (advisor) ; Hlávka, Zdeněk (referee)
In this thesis we investigate various methods for testing independence in two-way contingency tables. The methods are explained, their advantages and drawbacks are dis- cussed, and we also illustrate the methods on an example. Further, we compare the tests on simulated data using R statistic programming language. Based on simulation results we try to decide which test is the best choice for a situation. In particular, we investi- gate a new method, USP test, which is based on the theory of so called U-statistics. We therefore describe these, too. It is shown that USP test performs much better than other tests in particular cases, but fails in some others. These cases are specified and guidelines are made about when the test is advantageous to use and when it is not. 1
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Robust regularized regression
Krett, Jakub ; Kalina, Jan (advisor) ; Maciak, Matúš (referee)
This thesis is devoted to introducing various types of robust and regularized regression estimates. The aim of the thesis is to present a new LWS-lasso estimate that combines robustness and regularization at the same time. Firstly, basic concepts of linear regression and modifications of the least squares are explained. Then, various robust and regula- rized estimates are introduced along with the new LWS-lasso estimate and its software implementation. Subsequently, selected estimates are compared to each other on real data and in a simulation study. 1
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Robust regression and robust neural networks
Janáček, Patrik ; Kalina, Jan (advisor) ; Maciak, Matúš (referee)
The classical least squares approach in linear regression is prone to the presence of outliers in the data. The aim of this thesis is to present several robust alternatives to the least squares method in the linear regression framework and discuss their properties. Then robust neural networks based on these estimators are introduced and compared in a simulation study. In particular, the least weighted squares method with adaptive weights seems promising, as it is able to combine high robustness with efficiency in the absence of contamination in the data. 1
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Risk reserving based on ODP model
Procházka, Viktor ; Maciak, Matúš (advisor) ; Mazurová, Lucie (referee)
This thesis deals with estimating the outstanding claims reserve, one of important problems of insurance mathematics. It introduces the chain-ladder method as the ba- sic method for estimating the outstanding claims. Besides this method, it also presents models using the Poisson and ODP distributions to describe the increments of run-off triangles, which lead to identical point estimate of the outstanding claims reserve as the chain-ladder method. Additionally, this thesis deals with a simulation study concerned with the properties of these methods and the upper estimate of the outstanding claims in the Poisson and ODP models, where bootstrap estimate is also examined.
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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
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Selected approaches to seasonal adjustment of economic time series
Grätzer, Martin ; Hendrych, Radek (advisor) ; Maciak, Matúš (referee)
This thesis deals with the issue of seasonal adjustment of economic time series and their subsequent predictions. In the theoretical part we define the time series and its properties and describe the individual methods we will use: simple approaches, modeling using a qualitative variable, Holt-Winters method, Schlicht method and ETS methods. In the practical part we apply the presented methods to real economic time series. We will discuss the advantages and disadvantages of using the method and also look at the behavior of the error component. Subsequently, we will compare them according to the ability to predict the subsequent development of a given time series. 1
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Generalized Method of Moments
Volejníková, Viktorie ; Maciak, Matúš (advisor) ; Hušková, Marie (referee)
The topic of this bachelor thesis is the Generalized Method of Moments (GMM), its asymptotic properties, and its implementations. The first chapter briefly introduces the moment conditions and the Method of Moments (MM) which is then generalized to the GMM. In the second chapter, the consistency and the asymptotic normality of the GMM are proved and the optimal weight- ing matrix of the estimator is derived. The third chapter focuses on three implementations of the GMM: the Two-Step algorithm, the Iterated algorithm, and the Continuously updating procedure. In the fourth chapter, the accuracy of the MM and the GMM estimates is investigated and the GMM implementa- tions are compared. 1
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Analysis of shape of random functions
Fürst, Matouš ; Nagy, Stanislav (advisor) ; Maciak, Matúš (referee)
Registration of functional data is a part of functional data analysis which focuses on the transformation of a sample of functions such that the shapes of these functions are aligned and undesired variation between them removed. This thesis describes the general theory of functional registration and compares two selected methods. These two methods are thoroughly described, with a focus on their theoretical properties. Moreover, a modification of one of the methods is proposed. A comparison is performed on both real and simulated datasets, and an extension for registration into multiple groups is utilized. 1
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Variable selection based on penalized likelihood
Chlubnová, Tereza ; Kulich, Michal (advisor) ; Maciak, Matúš (referee)
Selection of variables and estimation of regression coefficients in datasets with the number of variables exceeding the number of observations consti- tutes an often discussed topic in modern statistics. Today the maximum penalized likelihood method with an appropriately selected function of the parameter as the penalty is used for solving this problem. The penalty should evaluate the benefit of the variable and possibly mitigate or nullify the re- spective regression coefficient. The SCAD and LASSO penalty functions are popular for their ability to choose appropriate regressors and at the same time estimate the parameters in a model. This thesis presents an overview of up to date results in the area of characteristics of estimates obtained by using these two methods for both small number of regressors and multidimensional datasets in a normal linear model. Due to the fact that the amount of pe- nalty and therefore also the choice of the model is heavily influenced by the tuning parameter, this thesis further discusses its selection. The behavior of the LASSO and SCAD penalty functions for different values and possibili- ties for selection of the tuning parameter is tested with various numbers of regressors on simulated datasets.
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