GeD spline estimation of multivariate Archimedean copulas
A new multivariate Archimedean copula estimation method is proposed in a non-parametric setting. The method uses the so-called Geometrically Designed splines (GeD splines) to represent the cdf of a random variable W[theta], obtained through the probability integral transform of an Archimedean copula with parameter [theta]. Sufficient conditions for the GeD spline estimator to possess the properties of the underlying theoretical cdf, K([theta],t), of W[theta], are given. The latter conditions allow for defining a three-step estimation procedure for solving the resulting non-linear regression problem with linear inequality constraints. In the proposed procedure, finding the number and location of the knots and the coefficients of the unconstrained GeD spline estimator and solving the constraint least-squares optimisation problem are separated. Thus, the resulting spline estimator is used to recover the generator and the related Archimedean copula by solving an ordinary differential equation. The proposed method is truly multivariate, it brings about numerical efficiency and as a result can be applied with large volumes of data and for dimensions d>=2, as illustrated by the numerical examples presented.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006.
"Efficient Estimation of Semiparametric Multivariate Copula Models,"
Journal of the American Statistical Association,
American Statistical Association, vol. 101, pages 1228-1240, September.
- Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004. "Efficient Estimation of Semiparametric Multivariate Copula Models," Vanderbilt University Department of Economics Working Papers 0420, Vanderbilt University Department of Economics.
- Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
- Genest, Christian & Rivest, Louis-Paul, 2001. "On the multivariate probability integral transformation," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 391-399, July.
- Lambert, Philippe, 2007. "Archimedean copula estimation using Bayesian splines smoothing techniques," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6307-6320, August.
- Peter Hall & Natalie Neumeyer, 2006. "Estimating a bivariate density when there are extra data on one or both components," Biometrika, Biometrika Trust, vol. 93(2), pages 439-450, June.
- Christian Genest & Jean-François Quessy & Bruno Rémillard, 2006. "Goodness-of-fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366.
- Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(03), pages 535-562, June.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3570-3582. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.