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Functional data analysis
Jurica, Tomáš ; Hlávka, Zdeněk (advisor) ; Hlubinka, Daniel (referee)
The aim of the master thesis is to review of reconstruction techniques of func- tional data and existing one-way functional ANOVA (FANOVA) tests. Specif- ically, the work deals with L2 -norm based and F-type mean functions equality tests, L2 -norm based covariance functions equality tests and tests for distri- bution equality. Furthermore, for each type of the test, it is introduced test based on reconstructed functional data, using orthornormal basis functions of L2 space. Finally, simulation study was conducted for comparing properties of tests using orthonormal basis representation of functional data and tests applied on non-reconstructed data. 1
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k-sample problem with ordered alternative
Nováková, Martina ; Hlávka, Zdeněk (advisor) ; Pešta, Michal (referee)
In this thesis we deal with k-sample problem with ordered alternative. At the beginning of the thesis isotonic regression is introduced. We use isotonic regression for maximum likelihood estimation of ordered parameters. In the second chapter, we describe the χ2 and E 2 tests that use the knowledge of isotonic regression and are based on the likelihood ratio. The exact null hypothesis distributions of their test statistics are derived in detail. The one-sided studentized range test is also further described. At the end of the thesis, we show the use of the E 2 test on the real data. 1
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Multiple comparison with controls
Sychova, Maryna ; Hlávka, Zdeněk (advisor) ; Komárek, Arnošt (referee)
The main theme of the diploma thesis is description of multiple comparison methods, which are used to compare pairs of means or medians. At the beggining we define multiple testing and describe methods that control the probability of first type error at level α. The Šidák method and the prerequi- sites required for its use are described in detail. The work also includes a brief description of analysis of variance and an overview of several methods of multiple comparison. Additionally, the method of multiple comparison with control, its modifications and practical implementation is presented.
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Levene's Test for Equality of Variances
Hrochová, Magdalena ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
In the presented bachelor thesis, we focused on the Levene's test and its modifications that are used to assess the equality of variances for k independent random samples. At the beginning, we described Analysis of variance (ANOVA) that is a method for analyzing differences between group means for k independent random samples. The following part contains the original Levene's test description, including a discussion about the assumptions' verification for using ANOVA. Considering the fact that the original test is not confident in case of samples from specific distributions (e.g. a chi-square distribution) we summarize some known and suggest some new modifications. The main part of the thesis is dedicated to experimental simulations. In the conclusion, we discuss the simulation results for different versions of the Levene's test and other similar tests for equality of variances. 1
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