Discipline of Applied Mathematics, The University of Adelaide, South Australia 5005, Australia. e-mail: glenis.crane@adelaide.edu.au
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CONDITIONAL EXPECTATION FORMULAE FOR COPULAS
Article first published online: 18 MAR 2008
DOI: 10.1111/j.1467-842X.2007.00499.x
2008 Australian Statistical Publishing Association Inc.
Additional Information
How to Cite
Crane, G. J. and Hoek, J. v. d. (2008), CONDITIONAL EXPECTATION FORMULAE FOR COPULAS. Australian & New Zealand Journal of Statistics, 50: 53–67. doi: 10.1111/j.1467-842X.2007.00499.x
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Discipline of Applied Mathematics, The University of Adelaide, South Australia 5005, Australia. e-mail: glenis.crane@adelaide.edu.au
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Mathematics and Statistics, University of South Australia, (City West Campus), GPO Box 2471, Adelaide, South Australia 5001, Australia.
Publication History
- Issue published online: 18 MAR 2008
- Article first published online: 18 MAR 2008
- Abstract
- Article
- References
- Cited By
Keywords:
- Archimedean copulas;
- conditional expectation;
- Farlie–Gumbel–Morgenstern copulas
Summary
Not only are copula functions joint distribution functions in their own right, they also provide a link between multivariate distributions and their lower-dimensional marginal distributions. Copulas have a structure that allows us to characterize all possible multivariate distributions, and therefore they have the potential to be a very useful statistical tool. Although copulas can be traced back to 1959, there is still much scope for new results, as most of the early work was theoretical rather than practical. We focus on simple practical tools based on conditional expectation, because such tools are not widely available. When dealing with data sets in which the dependence throughout the sample is variable, we suggest that copula-based regression curves may be more accurate predictors of specific outcomes than linear models. We derive simple conditional expectation formulae in terms of copulas and apply them to a combination of simulated and real data.