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
Date Written: April 2008
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: Suggested Citation