EFFICIENT ESTIMATION IN THE BIVARIATE NORMAL COPULA MODEL - NORMAL MARGINS ARE LEAST FAVORABLE

Consider semi-parametric bivariate copula models in which the family o f copula functions is parametrized by a Euclidean parameter theta of i nterest and in which the two unknown marginal distributions are the (i nfinite-dimensional) nuisance parameters. The efficient score for thet a can be characterized in terms of the solutions of two coupled Sturm- Liouville equations. Where the family of copula functions corresponds to the normal distributions with mean 0, variance 1 and correlation th eta, the solution of these equations is given, and we thereby show tha t the normal scores rank correlation coefficient is asymptotically eff icient. We also show that the bivariate normal model with equal varian ces constitutes the least favourable parametric submodel. Finally, we discuss the interpretation of \theta\ in the normal copula model as th e maximum (monotone) correlation coefficient.