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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Center-outward ranks and signs and their application in statistical tests
 Roubínová, Veronika ; Hudecová, Šárka (advisor) ; Hlubinka, Daniel (referee)
This thesis describes the theory of multivariate rank tests based on center-outward ranks and signs. The definition of the center-outward ranks and signs is based on the measure transportation problem and depends highly on the chosen underlying grid. Sev- eral ways to generate such grids are suggested. Center-outward ranks and signs are then used to construct various test statistics for one-sample testing of location. The main contribution of the work is the introduction of new variants of the one-sample test of location. The proposed test statistics are based on randomized signs and added zero with the usage of the permutation tests for obtaining p-values. The tests are constructed under the assumption of both central or angular symmetry of the underlying distribution. In the end, a simulation study is performed to illustrate the performance of the proposed tests under different settings for several alternatives. 1
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Trajectories of Fractional Brownian Motions
 Roubínová, Veronika ; Čoupek, Petr (advisor) ; Maslowski, Bohdan (referee)
This work concerns the fractional Brownian motion, in particular, the properties of its trajectories. Firstly some basic notions are defined and then the definiton of the fractional Brownian motion itself is given. Subsequently, its basic properties such as correlation of increments and self-similarity are derived. Continuity of its trajectories is shown using the Kolomogorov-Chentsov Theorem. The main chapter contains a thorough proof of the law of the iterated logarithm. It is complemented with simulations of limit behavior of trajectories and used to prove nondifferentiability. 1
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