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Statistické úlohy pro náhodné procesy
dc.contributor.advisorHlubinka, Daniel
dc.creatorKvitkovičová, Andrea
dc.date.accessioned2017-04-10T10:50:11Z
dc.date.available2017-04-10T10:50:11Z
dc.date.issued2008
dc.identifier.urihttp://hdl.handle.net/20.500.11956/14893
dc.description.abstractThe thesis deals with testing hypotheses about the parameters of the Wiener process with a constant drift rate and instantaneous variance. The tests are based on the first time, when the process reaches a pre-specified boundary point. We consider a process with a non-negative drift rate, and we observe hitting a positive point. We focus on tests about the drift rate, in particular about the absence of any drift. We first study several basic properties of the Wiener process and its connection with the Wiener process with a drift. Using these, we derive distributional properties of the first hitting time. We also describe selected hypotheses testing techniques in the setting of exponential families. We construct uniformly most powerful unbiased tests of one parameter in the presence of a nuisance parameter. Further, we construct uniformly most powerful tests of hypotheses about the drift rate, while the variance is known, and we study this situation in more detail. Finally, we construct asymptotic simultaneous tests of both parameters based on the R'enyi divergences.en_US
dc.languageEnglishcs_CZ
dc.language.isoen_US
dc.publisherUniverzita Karlova, Matematicko-fyzikální fakultacs_CZ
dc.titleStatistical inference for random processesen_US
dc.typediplomová prácecs_CZ
dcterms.created2008
dcterms.dateAccepted2008-05-15
dc.description.departmentDepartment of Probability and Mathematical Statisticsen_US
dc.description.departmentKatedra pravděpodobnosti a matematické statistikycs_CZ
dc.description.facultyMatematicko-fyzikální fakultacs_CZ
dc.description.facultyFaculty of Mathematics and Physicsen_US
dc.identifier.repId43638
dc.title.translatedStatistické úlohy pro náhodné procesycs_CZ
dc.contributor.refereeŠtěpán, Josef
dc.identifier.aleph000971514
thesis.degree.nameMgr.
thesis.degree.levelmagisterskécs_CZ
thesis.degree.disciplineProbability, mathematical statistics and econometricsen_US
thesis.degree.disciplinePravděpodobnost, matematická statistika a ekonometriecs_CZ
thesis.degree.programMatematikacs_CZ
thesis.degree.programMathematicsen_US
uk.thesis.typediplomová prácecs_CZ
uk.taxonomy.organization-csMatematicko-fyzikální fakulta::Katedra pravděpodobnosti a matematické statistikycs_CZ
uk.taxonomy.organization-enFaculty of Mathematics and Physics::Department of Probability and Mathematical Statisticsen_US
uk.faculty-name.csMatematicko-fyzikální fakultacs_CZ
uk.faculty-name.enFaculty of Mathematics and Physicsen_US
uk.faculty-abbr.csMFFcs_CZ
uk.degree-discipline.csPravděpodobnost, matematická statistika a ekonometriecs_CZ
uk.degree-discipline.enProbability, mathematical statistics and econometricsen_US
uk.degree-program.csMatematikacs_CZ
uk.degree-program.enMathematicsen_US
thesis.grade.csVýborněcs_CZ
thesis.grade.enExcellenten_US
uk.abstract.enThe thesis deals with testing hypotheses about the parameters of the Wiener process with a constant drift rate and instantaneous variance. The tests are based on the first time, when the process reaches a pre-specified boundary point. We consider a process with a non-negative drift rate, and we observe hitting a positive point. We focus on tests about the drift rate, in particular about the absence of any drift. We first study several basic properties of the Wiener process and its connection with the Wiener process with a drift. Using these, we derive distributional properties of the first hitting time. We also describe selected hypotheses testing techniques in the setting of exponential families. We construct uniformly most powerful unbiased tests of one parameter in the presence of a nuisance parameter. Further, we construct uniformly most powerful tests of hypotheses about the drift rate, while the variance is known, and we study this situation in more detail. Finally, we construct asymptotic simultaneous tests of both parameters based on the R'enyi divergences.en_US
uk.publication.placePrahacs_CZ
uk.grantorUniverzita Karlova, Matematicko-fyzikální fakulta, Katedra pravděpodobnosti a matematické statistikycs_CZ


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