Copula modeling has gained much attention in many fields recently with the advantage of separating dependence structure from marginal distributions. In real data, however, serious ties are often present in one or multiple margins, which cause problems to many rank-based statistical methods developed under the assumption of continuous data with no ties. Simple methods such as breaking the ties at random or using average rank introduce independence into the data and, hence, lead to biased estimation. We propose an estimation method that treats the ranks of tied data as being interval censored and maximizes a pseudo-likelihood based on interval censored pseudo-observations. A parametric bootstrap procedure that preserves the observed tied ranks in the data is adapted to assess the estimation uncertainty and perform goodness-of-fit tests. The proposed approach is shown to be very competitive in comparison to the simple treatments in a large scale simulation study. Application to a bivariate insurance data illustrates the methodology.

中文翻译：

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具有关系的数据的 Copula 建模

最近，Copula 建模以其将依赖结构与边缘分布分离的优势在许多领域得到了广泛关注。然而，在实际数据中，严重的联系往往存在于一个或多个边缘，这给许多在连续数据没有联系的假设下开发的基于秩的统计方法带来了问题。简单的方法，例如随机打破联系或使用平均等级，将独立性引入数据中，从而导致估计有偏差。我们提出了一种估计方法，将绑定数据的等级视为区间删失，并基于区间删失伪观察最大化伪似然。保留数据中观察到的绑定等级的参数引导程序适用于评估估计不确定性并执行拟合优度测试。与大规模模拟研究中的简单处理相比，所提出的方法显示出非常有竞争力。双变量保险数据的应用说明了该方法。