Robustness of a semiparametric estimator of a copula

Copulas offer a convenient way of modelling multivariate observations and capturing the intrinsic dependence between the components of a multivariate random variable. A semiparametric method for estimating the dependence parameters of copulas was proposed by Genest, Ghoudi and Rivest (1995), in which the marginal distributions are estimated nonparameterically by empirical distribution functions. Thus, this method does not require any marginal distribution to have a known parametric form. However, a standard concern about semiparametric methods is the possibility that it may be substantially less efficient than the parametric method when the model is completely parametric and correctly specified. In this paper we investigate the efficiency-robustness properties of the foregoing semiparametric method by simulation; in particular, we evaluate the performance of this method when the marginal distributions are specified correctly and when they are specified incorrectly. The results show that the semiparametric method is better than the parametric methods. An example involving the household expenditure data for Australia is used to compare and contrast the methods