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Functional ANOVA
Dolník, Viktor ; Dvořák, Jiří (advisor) ; Nagy, Stanislav (referee)
We introduce the concept of functional data and the problem of functional analysis of variance, which differs from the univariate case in the fact that random functions, not random variables, are the subject of comparison. We continue by deriving an asymptotic test for functional one-way ANOVA from the elementary univariate F-test. We describe the simulation envelope test, whose global version suffers from the multiple comparisons problem. Then, an ordering is defined, based on which we create the rank envelope test, a stronger alternative to the simulation envelope test. We also describe how the rank test can be interpreted graphically. Using the rank envelope test, we devise another test for functional one-way ANOVA, which is also graphically interpretable and thus does not need a post-hoc analysis to identify which groups caused rejection of the null hypothesis. We compare the one-way ANOVA tests on a real-case study and a simulation study. 1
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Functional ANOVA
Dolník, Viktor ; Dvořák, Jiří (advisor) ; Nagy, Stanislav (referee)
We introduce the concept of functional data and the problem of functional analysis of variance, which differs from the univariate case in the fact that random functions, not random variables, are the subject of comparison. We continue by deriving an asymptotic test for functional one-way ANOVA from the elementary univariate F-test. We describe the simulation envelope test, whose global version suffers from the multiple comparisons problem. Then, an ordering is defined, based on which we create the rank envelope test, a stronger alternative to the simulation envelope test. We also describe how the rank test can be interpreted graphically. Using the rank envelope test, we devise another test for functional one-way ANOVA, which is also graphically interpretable and thus does not need a post-hoc analysis to identify which groups caused rejection of the null hypothesis. We compare the one-way ANOVA tests on a real-case study and a simulation study. 1
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Exact envelope tests
Maděřičová, Soňa ; Dvořák, Jiří (advisor) ; Beneš, Viktor (referee)
In this work we are focusing on Monte Carlo simulation tests, in particular we are dealing with envelope and deviation tests. We describe the development of envelope tests from standard envelope tests, in which we can not control significance level, through refined envelope tests, where we can control the significance level indirectly, to exact envelope tests, for which the significance level can be chosen in advance. We will show how the exact envelope tests are related to deviation tests. Further we compare individual kinds of tests using examples and describe their advantages and disadvantages.
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