Thesis (MComm (Statistics and Actuarial Science))--Stellenbosch University, 2008. / The 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/3298 |
| Date | 12 1900 |
| Creators | Kpanzou, Tchilabalo Abozou |
| Contributors | De Wet, Tertius, Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | Stellenbosch University |
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