Rank-Based Semiparametric Efficient Estimator for General Copula Models

For copula models with unknown marginal distributions and an unspecified Euclidean parameter, a natural way to get a rank-based semiparametrically efficient estimator for the Euclidean parameter is to solve the estimating equation constructed using the efficient score, with the unknown marginal distribution functions substituted by the empirical versions. However, the solution may lack a closed form and may only be approximate. At present, it is not known how a rank-based semiparametrically efficient estimator can be found for general copula models. By using a given arbitrary consistent rank-based estimator as the initial point, the authors propose a K-step estimator that is more efficient, where K is related to the convergence rate of the initial point. The authors show that, under regularity conditions, the K-step estimator achieves the semiparametric efficiency bound for general copula models. Numerical calculation methods are also presented. Finally, the authors perform simulations to demonstrate the superiority of the proposed method.