Aspects of copulas and goodness-of-fit

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dc.contributor.advisorDe Wet, Tertiusen_ZA
dc.contributor.authorKpanzou, Tchilabalo Abozouen_ZA
dc.contributor.otherStellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
dc.date.accessioned2008-11-25T08:24:58Zen_ZA
dc.date.accessioned2010-07-09T11:07:16Z
dc.date.available2008-11-25T08:24:58Zen_ZA
dc.date.available2010-07-09T11:07:16Z
dc.date.issued2008-12en_ZA
dc.descriptionThesis (MComm (Statistics and Actuarial Science))--Stellenbosch University, 2008.en_ZA
dc.description.abstractThe goodness-of- t of a statistical model describes how well it ts a set of observations. Measures of goodness-of- t typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, for example to test for normality, to test whether two samples are drawn from identical distributions, or whether outcome frequencies follow a speci ed distribution. Goodness-of- t for copulas is a special case of the more general problem of testing multivariate models, but is complicated due to the di culty of specifying marginal distributions. In this thesis, the goodness-of- t test statistics for general distributions and the tests for copulas are investigated, but prior to that an understanding of copulas and their properties is developed. In fact copulas are useful tools for understanding relationships among multivariate variables, and are important tools for describing the dependence structure between random variables. Several univariate, bivariate and multivariate test statistics are investigated, the emphasis being on tests for normality. Among goodness-of- t tests for copulas, tests based on the probability integral transform, Rosenblatt's transformation, as well as some dimension reduction techniques are considered. Bootstrap procedures are also described. Simulation studies are conducted to rst compare the power of rejection of the null hypothesis of the Clayton copula by four di erent test statistics under the alternative of the Gumbel-Hougaard copula, and also to compare the power of rejection of the null hypothesis of the Gumbel-Hougaard copula under the alternative of the Clayton copula. An application of the described techniques is made to a practical data set.en_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/3298
dc.language.isoenen_ZA
dc.publisherStellenbosch : Stellenbosch University
dc.rights.holderStellenbosch University
dc.subjectGoodness-of-fit testsen_ZA
dc.subjectCopulas (Mathematical statistics)en_ZA
dc.subjectTest statisticen_ZA
dc.subjectPower of a testen_ZA
dc.subjectDissertations -- Statistics and actuarial scienceen
dc.subjectTheses -- Statistics and actuarial scienceen
dc.titleAspects of copulas and goodness-of-fiten_ZA
dc.typeThesisen_ZA
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