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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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Evaluation of quality of life in terms of poverty rates
Brázdilová, Michaela ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
This bachelor thesis deals with the evaluation of quality of life in terms of poverty rates. The aim is to define how social conditions of population affect subjective perceptions of quality of life. The paper provides an overview of the most important researches in this area, of which Survey on perception of quality of life in 75 European cities and survey Income and Living Conditions are analysed in detail. The dependence of a problem of poverty on other social indicators is investigated. The last chapter is devoted to calculations of poverty rates, especially at risk of poverty rate, but there are other indicators of poverty mentioned in terms of income inequality. In the summary, there is a poverty index presented as one possible indicator of social quality of life.
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Surveys of quality of life
Šištíková, Markéta ; Malá, Ivana (advisor) ; Vild, Jiří (referee)
The main aim of this bachelor thesis is to describe creation and evaluation of surveys, including selection of respondents and accurate formulation of the questionnaire. Thesis is focused on marketing and an medical environment and in relation to the quality of life survey. Endeavor of this thesis is to define quality of life for questionnaires examination creation. There are described the most important questionnaire examination of quality of life, that are known throughout the world and are used nowadays (questionnaire SF-36, EORTC QLQ-C30, EORTC QLQ-CX24, EG-5D).
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Statistical analysis of results from the subject 4ST201
Novák, Miroslav ; Čabla, Adam (advisor) ; Malá, Ivana (referee)
The main goal of this bachelor thesis is the statistical comparison of results from students who attended the course Statistika at the University of Economics in Prague. The thesis is divided into two main parts. The first part is concentrated on the results of students in winter semester of the academic year 2011/2012. This part is mainly focused on mid-term tests throughout semester. In the second part I compare results of students in the summer and winter semester, to this comparison I used data from summer semeseter 2010/2011 and data from winter semester 2011/2012. The small theoretical overview does not miss in the beginning and in the conclusion we can find the summary of all findings and calculations.
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