Copulas have been known in the statistical literature for many years, and
have become useful tools in modeling dependence structure of multivariate
random variables, overcoming some of the drawbacks of the commonly-used
correlation measures. Goodness-of-fit tests for copulas play a very important
role in evaluating the suitability of a potential input copula model. In recent
years, many approaches have been proposed for constructing goodness-of-fit
tests for copula families. Among them, the so-called “blanket tests" do not
require an arbitrary data categorization or any strategic choice of weight function, smoothing parameter, kernel, and so on.
As preliminaries, some background and related results of copulas are firstly
presented. Three goodness-of-fit test statistics belonging to the blanket test
classification are then introduced. Since the asymptotic distributions of the
test statistics are very complicated, parametric bootstrap procedures are employed to approximate critical values of the test statistics under the null hypotheses. To assess the performance of the three test statistics in the low
dependence cases, simulation studies are carried out for three bivariate copula families, namely the Gumbel-Hougaard copula family, the Ali-Mikhail-Haq
copula family, and the Farlie-Gumbel-Morgenstern copula family. Specifically
the effect of low dependence on the empirical sizes and powers of the three
blanket tests under various combinations of null and alternative copula families are examined. Furthermore, to check the performance of the three tests
for higher dimensional copulas, the simulation studies are extended to some
three-dimensional copulas. Finally the three goodness-of-fit tests are applied
to two real data sets. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy
| Identifer | oai:union.ndltd.org:HKU/oai:hub.hku.hk:10722/174554 |
| Date | January 2012 |
| Creators | Lü, Wei, 吕薇 |
| Publisher | The University of Hong Kong (Pokfulam, Hong Kong) |
| Source Sets | Hong Kong University Theses |
| Language | English |
| Detected Language | English |
| Type | PG_Thesis |
| Source | http://hub.hku.hk/bib/B47849964 |
| Rights | The author retains all proprietary rights, (such as patent rights) and the right to use in future works., Creative Commons: Attribution 3.0 Hong Kong License |
| Relation | HKU Theses Online (HKUTO) |
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