Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-09T22:24:11.318Z Has data issue: false hasContentIssue false
  • English
  • Français

STATISTICAL INFERENCE FOR COPULAS IN HIGH DIMENSIONS: A SIMULATION STUDY

Published online by Cambridge University Press:  18 June 2013

Paul Embrechts  and
Marius Hofert
Paul Embrechts*
Affiliation:
RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
Marius Hofert
Affiliation:
RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland, E-Mail: [email protected]
*
E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Statistical inference for copulas has been addressed in various research papers. Due to the complicated theoretical results, studies have been carried out mainly in the bivariate case, be it properties of estimators or goodness-of-fit tests. However, from a practical point of view, higher dimensions are of interest. This work presents the results of large-scale simulation studies with particular focus on the question to what extent dimensionality influences point and interval estimators.

Keywords

Maximum likelihood estimatorinference functions for marginsmaximum pseudo-likelihood estimatorKendall's tau estimatorconfidence intervalshigh dimensions
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 2 , May 2013 , pp. 81 - 95
Copyright
Copyright © ASTIN Bulletin 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arbenz, P., Hummel, C. and Mainik, G. (2012) Copula based hierarchical risk aggregation through sample reordering. Insurance: Mathematics and Economics, 51, 122–133.Google Scholar
Bellman, R.E. (1957) Dynamic Programming. Princeton, NJ: Princeton University Press.Google ScholarPubMed
Berg, D. (2009) Copula goodness-of-fit testing: An overview and power comparison. The European Journal of Finance, 15, 675–701.CrossRefGoogle Scholar
Bühlmann, P. and van de Geer, S. (2011) Statistics for High-Dimensional Data. Springer.CrossRefGoogle Scholar
Davison, A.C. (2003) Statistical Models. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Dobrić, J. and Schmid, F. (2007) A goodness of fit test for copulas based on Rosenblatt's transformation. Computational Statistics & Data Analysis, 51, 4633–4642.CrossRefGoogle Scholar
Genest, C., Ghoudi, K. and Rivest, L.-P. (1995) A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika, 82 (3), 543–552.CrossRefGoogle Scholar
Genest, C., Rémillard, B. and Beaudoin, D. (2009) Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics, 44, 199–213.Google Scholar
Genest, C. and Rivest, L.-P. (1993) Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association, 88 (423), 1034–1043.CrossRefGoogle Scholar
Genest, C. and Werker, B.J.M. (2002) Conditions for the asymptotic semiparametric efficiency of an omnibus estimator of dependence parameters in copula models. In Distributions with Given Marginals and Statistical Modelling (ed. Cuadras, C.M., Fortiana, J. and Rodríguez-Lallena, J.A.), pp. 103–112. Dordrecht: Kluwer.CrossRefGoogle Scholar
Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed. Springer.CrossRefGoogle Scholar
Hofert, M., Mächler, M. and McNeil, A.J. (2012) Likelihood inference for Archimedean copulas in high dimensions under known margins. Journal of Multivariate Analysis, 110, 133–150.CrossRefGoogle Scholar
Hofert, M. and Scherer, M. (2011) CDO pricing with nested Archimedean copulas. Quantitative Finance, 11 (5), 775–787.CrossRefGoogle Scholar
Jaworski, P., Durante, F., Härdle, W.K. and Rychlik, T. (eds.) (2010) Copula Theory and Its Applications. Lecture Notes in Statistics – Proceedings, vol. 198. Springer.CrossRefGoogle Scholar
Joe, H. and Xu, J.J. (1996) The Estimation Method of Inference Functions for Margins for Multivariate Models. Technical Report 166, Department of Statistics, University of British Columbia.Google Scholar
Kim, G., Silvapulle, M.J. and Silvapulle, P. (2007) Comparison of semiparametric and parametric methods for estimating copulas. Computational Statistics & Data Analysis, 51, 2836–2850.CrossRefGoogle Scholar
Kojadinovic, I. and Yan, J. (2010a) Comparison of three semiparametric methods for estimating dependence parameters in copula models. Insurance: Mathematics and Economics, 47, 52–63.Google Scholar
Kojadinovic, I. and Yan, J. (2010b) Modeling multivariate distributions with continuous margins using the copula R package. Journal of Statistical Software, 34 (9), 1–20.CrossRefGoogle Scholar
Lee, A.J. (1990). U-Statistics: Theory and Practice. Dekker.Google Scholar
McNeil, A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques, Tools. Princeton, NJ: Princeton University Press.Google Scholar
Portnoy, S. (1988) Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity. The Annals of Statistics, 16 (1), 356–366.CrossRefGoogle Scholar
Savu, C. and Trede, M. (2010) Hierarchies of Archimedean copulas. Quantitative Finance, 10 (3), 295–304.CrossRefGoogle Scholar
Tsukahara, H. (2005) Semiparametric estimation in copula models. The Canadian Journal of Statistics, 33 (3), 357–375.CrossRefGoogle Scholar
Weiß, G.N.F. (2010) Copula parameter estimation: Numerical considerations and implications for risk management. The Journal of Risk, 13 (1), 17–53.CrossRefGoogle Scholar