Maximum pseudo-likelihood (MPL) is a semiparametric estimation method often used to obtain the dependence parameters in copula models from data. It has been shown that despite being consistent, and in same cases efficient, MPL estimation can overestimate the level of dependence especially for small weakly dependent samples. We show that the MPL method uses the expected value of order statistics and we propose to use instead the median or the mode of the same order statistics. In a simulation study we compare the finite-sample performance of the proposed estimators with that of the original MPL and the inversion method estimators based on Kendall's tau and Spearman's rho. Our results indicate that the modified MPL estimators, especially the one based on the mode of the order statistics, have better finite-sample performance and still enjoy the large-sample properties of the original MPL method.

中文翻译：

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小型弱相关样本的 copula 模型中的最大伪似然估计

最大伪似然（MPL）是一种半参数估计方法，常用于从数据中获取 copula 模型中的依赖参数。已经表明，尽管 MPL 估计是一致的，并且在相同的情况下是有效的，但 MPL 估计可能会高估依赖程度，尤其是对于小的弱依赖样本。我们展示了 MPL 方法使用顺序统计的期望值，我们建议使用中位数或相同顺序统计的众数。在模拟研究中，我们将所提出的估计器的有限样本性能与原始 MPL 和基于 Kendall tau 和 Spearman rho 的反演方法估计器的有限样本性能进行了比较。我们的结果表明，修改后的 MPL 估计器，尤其是基于订单统计模式的估计器，