Abstract In this work, we study the problem of (sub)copula estimation via continuity of the Sklar's correspondence. One benefit of this approach is that the estimator can be obtained from that of the corresponding (joint) distribution function via plug-in method. Additional proof is not required. Our approach is to naturally embed the space of subcopulas into the space of distribution functions. This allows us to consider two common modes of convergence, namely, the uniform convergence and the weak convergence on the space of (sub)copulas. Since these modes of convergence are well-studied, we will be able to combine our results with existing results in the same way that is done for distribution functions. Instead of proving these results directly, however, we will apply two common distances characterizing these modes of convergence, namely, the Chebyshev distance and the Levy distance. By using distances, the rate of convergence is also known. Topological properties of the space of subcopulas based on these two distances are also compared and contrasted with that of previously defined distances.

中文翻译：

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关于subcopula的一种分布形式

摘要 在这项工作中，我们通过 Sklar 对应关系的连续性研究（子）copula 估计问题。这种方法的一个好处是可以通过插件方法从相应（联合）分布函数的估计量中获得估计量。不需要额外的证明。我们的方法是将 subcopula 的空间自然地嵌入到分布函数的空间中。这使我们可以考虑两种常见的收敛模式，即（子）copulas 空间上的一致收敛和弱收敛。由于对这些收敛模式进行了充分研究，我们将能够以与分布函数相同的方式将我们的结果与现有结果相结合。然而，我们将应用表征这些收敛模式的两个共同距离，而不是直接证明这些结果，即，切比雪夫距离和列维距离。通过使用距离，收敛速度也是已知的。基于这两个距离的 subcopula 空间的拓扑特性也与先前定义的距离的拓扑特性进行了比较和对比。