cient Estimation in the Bivariate Normal Copula

Consider semiparametric bivariate copula models in which the family of copula functions is parametrized by a Euclidean parameter of interest and in which the two unknown marginal distributions are the in nite dimensional nuisance parameters The e cient score for can be characterized in terms of the solutions of two coupled Sturm Liouville equations In case the family of copula functions corresponds to the normal distributions with mean variance and correlation the solution of these equations is given and we thereby show that the Van der Waerden normal scores rank correlation coe cient is asymptotically e cient We also show that the bivariate normal model with equal variances constitutes the least favorable parametric submodel Finally we discuss the interpretation of j j in the normal copula model as the maximum monotone correlation coe cient Research supported in part by National Science Foundation grant DMS NATO NWO Grant B and by NIAID grant R AI AMS subject classi cations Primary G E secondary G H