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Selected problems and methods in multivariate data analysis
Goduľová, Lenka ; Zichová, Jitka (advisor) ; Hurt, Jan (referee)
Title: Selected problems and methods in multivariate data analysis Author: Lenka Goduľová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr. Abstract: The bachelor thesis deals with processing multidimensional data. The task was to apply selected methods on financial data. The thesis is composed of the theoretical section and the analysis of a particular database. The first four chapters deal with basic relations and definitions concerning random vector and variable, multidimensional data and the independence test in a contingency table. The following section is devoted to defining the particular methods selected: cluster analysis and discriminant analysis. In the practical section these methods are applied to a database of clients of a German bank. Keywords: random vector, multivariate distribution, multivariate random variable, contingency table, cluster analysis, discriminant analysis.
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Bilevel optimization problems and their applications to portfolio selection
Goduľová, Lenka ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
Title: Bilevel optimization problems and their applications to portfolio selection Author: Lenka Godul'ová Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D. Abstract: This work deals with the problem of bilevel tasks. First, it recalls the basic knowledge of mean-risk models, risk measure in singlelevel problems, and second degree stochastic dominance. Then it presents basic knowledge of bilevel tasks. bilevel problems have several advantages over singlelevel. In one process, it is possible to analyze two different or even conflicting situations. The bilevel role can better capture the relationship between the two objects. The main focus of the thesis is the formulation of various bilevel tasks and their reformulation into the simplest form. The numerical part deals with four types of formulated bilevel problems at selected risk measures. Keywords: Bilevel problems, Second degree stochastic dominance, Risk measures 1
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Bilevel optimization problems and their applications to portfolio selection
Goduľová, Lenka ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
Title: Bilevel optimization problems and their applications to portfolio selection Author: Lenka Godul'ová Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D. Abstract: This work deals with the problem of bilevel tasks. First, it recalls the basic knowledge of mean-risk models, risk measure in singlelevel problems, and second degree stochastic dominance. Then it presents basic knowledge of bilevel tasks. bilevel problems have several advantages over singlelevel. In one process, it is possible to analyze two different or even conflicting situations. The bilevel role can better capture the relationship between the two objects. The main focus of the thesis is the formulation of various bilevel tasks and their reformulation into the simplest form. The numerical part deals with four types of formulated bilevel problems at selected risk measures. Keywords: Bilevel problems, Second degree stochastic dominance, Risk measures 1
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Selected problems and methods in multivariate data analysis
Goduľová, Lenka ; Zichová, Jitka (advisor) ; Hurt, Jan (referee)
Title: Selected problems and methods in multivariate data analysis Author: Lenka Goduľová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr. Abstract: The bachelor thesis deals with processing multidimensional data. The task was to apply selected methods on financial data. The thesis is composed of the theoretical section and the analysis of a particular database. The first four chapters deal with basic relations and definitions concerning random vector and variable, multidimensional data and the independence test in a contingency table. The following section is devoted to defining the particular methods selected: cluster analysis and discriminant analysis. In the practical section these methods are applied to a database of clients of a German bank. Keywords: random vector, multivariate distribution, multivariate random variable, contingency table, cluster analysis, discriminant analysis.
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