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Analysis of time series of property criminal acts in the Czech Republic regions in the period 1994-2014
Kubiš, Miroslav ; Helman, Karel (advisor) ; Malá, Ivana (referee)
The bachelor thesis is examining annual and monthly time series of criminality in regions of the Czech Republic in the period from 1994 to 2014. For this thesis the data on property criminality were selected. The data were gained from Police office. The main aim of this thesis is to examine the development of these time series. For this analysis I use basic characteristics and some methods for modelling the seasonal component. Ambitions of this thesis are: to examine the amount of criminal records committed throughout the months of the year, to examine the development of all criminal records and to compare time series in the regions of the Czech Republic.
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Quantile Regression
Procházka, Jiří ; Bašta, Milan (advisor) ; Malá, Ivana (referee)
The thesis deals with brief introduction of the quantile regression theory. The thesis is divided into three thematic parts. In the first part the thesis deals with general introduction to the quantile regression, with theoretical aspects regarding quantile regression and with basic approaches to estimation of quantile regression parameters. The second part of the thesis focuses on general and asymptotic properties of the quantile regression. Goal of this part is to compare the quantile regression with traditional OLS regression and outline its possible application. In the third part the thesis describes statistical inference, construction of the confidence intervals and testing statistical hypotheses about quantile regression parameters. The goal of this part is to introduce traditional approach and the approach based on resampling procedures and in the end of the day perform mutual comparison of different approaches eventually propose partial modification.
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Analysis of household consumption in the EU
Kolman, Martin ; Bílková, Diana (advisor) ; Malá, Ivana (referee)
The goal of this work is to analyze the evolution of household consumption of the states in the EU. The consumption will be researched in the view of classification COICOP, which is the classification of individual consumption by purpose. After mapping of this evolution the estimation of future values will be done from known time series. This estimation will be performed by two different ways. First one will respect the composition of household consumption in sections of classification COICOP. The second one will only work with time series of average consumption for all sections together. To compare the states cluster analysis will be done. This analysis will be done by two ways again. First one will be aimed to analyze the current situation and the second one will be aimed to analyze the evolution of household consumption. Instead of Microsoft Excel STATGRAPHICS X64 CENTURION and SPSS will be used in this thesis. Household consumption prognosis is the main benefit of this thesis. This prognosis is made for all sections of COICOP. Analysis has shown, that the consumption should rise in future. There are few exceptions, mainly countries with not good economic situation as Greece.
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Nonlinear regression in R programming langure
Dolák, Martin ; Malá, Ivana (advisor) ; Bašta, Milan (referee)
This thesis deals with solutions of nonlinear regression problems using R programming language. The introductory theoretical part is devoted to familiarization with the principles of solving nonlinear regression models and of their applications in the program R. In both, theoretical and practical part, the most famous and used differentiator algorithms are presented, particularly the Gauss-Newton's and of the steepest descent method, for estimating the parameters of nonlinear regression. Further, in the practical part, there are some demo solutions of particular tasks using nonlinear regression methods. Overall, a large number of graphs processed by the author is used in this thesis for better comprehension.
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Gaussian mixtures in R
Marek, Petr ; Malá, Ivana (advisor) ; Zimmermann, Pavel (referee)
Using Gaussian mixtures is a popular and very flexible approach to statistical modelling. The standard approach of maximum likelihood estimation cannot be used for some of these models. The estimates are, however, obtainable by iterative solutions, such as the EM (Expectation-Maximization) algorithm. The aim of this thesis is to present Gaussian mixture models and their implementation in R. The non-trivial case of having to use the EM algorithm is assumed. Existing methods and packages are presented, investigated and compared. Some of them are extended by custom R code. Several exhaustive simulations are run and some of the interesting results are presented. For these simulations, a notion of usual fit is presented.
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Utilizing Bootstrap and Cross-validation for prediction error estimation in regression models
Lepša, Ondřej ; Bašta, Milan (advisor) ; Malá, Ivana (referee)
Finding a well-predicting model is one of the main goals of regression analysis. However, to evaluate a model's prediction abilities, it is a normal practice to use criteria which either do not serve this purpose, or criteria of insufficient reliability. As an alternative, there are relatively new methods which use repeated simulations for estimating an appropriate loss function -- prediction error. Cross-validation and bootstrap belong to this category. This thesis describes how to utilize these methods in order to select a regression model that best predicts new values of the response variable.
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Mixture distributions
Nedvěd, Jakub ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
Object of this thesis is to construct a mixture model of earnings of the Czech households. In first part are described characteristics of mixtures of statistical distributions with the focus on the mixtures of normal distibutions. In practical part of this thesis are constructed models with parameters extimations based on the data from EU-SILC. Models made by graphical method, EM algorithm and method of maximum likelihood. The quality of models is measured by Akaike information criterion.
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Length of doctoral studies at the Faculty of Informatics and Statistics
Hybšová, Aneta ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
This thesis describes the survival analysis, exactly Kaplan-Meier estimate. A main part of the thesis deals with the problem of censored data, which is typical for survival analysis. The empirical part describes lenght of PhD studies at the Faculty of Informatics and Statistics and their "survival" in studies by Kaplan-Meier curves. First are analyzed uncensored data and then the whole data set (censored and uncensored data).
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Analysis of results in the Statistics course, 4ST201
Krajča, Marek ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
The main objective of my bachelor thesis is to describe the discrepancy of students' results in the Statistics course, 4ST201. I hope to highlight the differences of student results between the winter semester of 2010/2011, summer semester of 2010/2011, and the winter semester of 2011/2012, during which a new structure of final examination was introduced. I will begin with a detailed discussion and analysis of results between the three aforementioned testing periods, and I hope to conclude by offering a hypothesis of discrepancies between the old and new testing structures.
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