We consider a general multivariate model where univariate marginal distributions are known up to a parameter vector and we are interested in estimating that parameter vector without specifying the joint distribution, except for the marginals. If we assume independence between the marginals and maximize the resulting quasi-likelihood, we obtain a consistent but inefficient QMLE estimator. If we assume a parametric copula (other than independence) we obtain a full MLE, which is efficient but only under a correct copula specification and may be biased if the copula is misspecified. Instead we propose a sieve MLE estimator (SMLE) which improves over QMLE but does not have the drawbacks of full MLE. We model the unknown part of the joint distribution using the Bernstein-Kantorovich polynomial copula and assess the resulting improvement over QMLE and over misspecified FMLE in terms of relative efficiency and robustness. We derive the asymptotic distribution of the new estimator and show that it reaches the relevant semiparametric efficiency bound. Simulations suggest that the sieve MLE can be almost as efficient as FMLE relative to QMLE provided there is enough dependence between the marginals. We demonstrate practical value of the new estimator with several applications. First, we apply SMLE in an insurance context where we build a flexible semi-parametric claim loss model for a scenario where one of the variables is censored. As in simulations, the use of SMLE leads to tighter parameter estimates. Next, we consider financial risk management examples and show how the use of SMLE leads to superior Value-at-Risk predictions. The paper comes with an online archive which contains all codes and datasets.

翻译：我们考虑一类一般多元模型，其中单变量边际分布已知至参数向量，且我们感兴趣的是在仅知边际分布而无需设定联合分布的情况下估计该参数向量。若假设边际间相互独立并最大化由此得到的拟似然函数，可获得一致但非高效的QMLE估计量；若假设参数化连接函数（而非独立结构），则可得到完全MLE估计量，该估计量在连接函数设定正确时具有高效性，但若连接函数设定错误则可能产生偏差。为此，我们提出筛MLE估计量（SMLE），它在改进QMLE的同时避免了完全MLE的缺陷。我们采用Bernstein-Kantorovich多项式连接函数对联合分布中的未知部分进行建模，并从相对效率和稳健性两个方面评估其对QMLE及错误设定FMLE的改进效果。我们推导了新估计量的渐近分布，证明其达到了相关半参数效率界。数值模拟表明，当边际间存在足够强的相依性时，筛MLE相对于QMLE的效率可接近FMLE。我们通过多个应用案例展示了新估计量的实用价值：首先，在保险场景中建立包含删失变量的灵活半参数索赔损失模型，与模拟结果一致，SMLE可获得更紧凑的参数估计；其次，在金融风险管理案例中，SMLE可显著提升风险价值预测的精度。本文附有在线归档文件，包含所有代码与数据集。