Improving Upon the Marginal Empirical Distribution Function When the Copula is Known

CentER Discussion Paper Series No. 2008-40

25 Pages Posted: 21 Apr 2008

See all articles by Johan Segers

Johan Segers

Catholic University of Louvain (UCL)

Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Date Written: April 2008

Abstract

At the heart of the copula methodology in statistics is the idea of separating marginal distributions from the dependence structure. However, as shown in this paper, this separation is not to be taken for granted: in the model where the copula is known and the marginal distributions are completely unknown, the empirical distribution functions are semi-parametrically efficient if and only if the copula is the independence copula. Incorporating the knowledge of the copula into a nonparametric likelihood yields an estimation procedure which by simulations shown to outperform the empirical distribution functions, the amount of improvement depending on the copula. Although the known-copula model is arguably artificial, it provides an instructive stepping stone to the more general model of a parametrically specified copula and arbitrary margins.

Keywords: independence copula, nonparametric maximum likelihood estimator, score function, semiparametric efficiency, tangent space

JEL Classification: C14

Suggested Citation

Segers, Johan and Van den Akker, Ramon and Werker, Bas J.M., Improving Upon the Marginal Empirical Distribution Function When the Copula is Known (April 2008). CentER Discussion Paper Series No. 2008-40, Available at SSRN: https://ssrn.com/abstract=1123502 or http://dx.doi.org/10.2139/ssrn.1123502

Johan Segers (Contact Author)

Catholic University of Louvain (UCL) ( email )

Place Montesquieu, 3
Louvain-la-Neuve, 1348
Belgium
+32 10 474311 (Phone)
+32 10 473032 (Fax)

HOME PAGE: http://www.uclouvain.be/stat

Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR ( email )

K-623
PO Box 90153
Tilburg, 5000 LE
Netherlands

HOME PAGE: http://sites.google.com/site/rvdnakker/

Bas J.M. Werker

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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