A key tool to carry out inference on the unknown copula when modeling a continuous multivariate distribution is a nonparametric estimator known as the empirical copula. One popular way of approximating its sampling distribution consists of using the multiplier bootstrap. The latter is however characterized by a high implementation cost. Given the rank-based nature of the empirical copula, the classical empirical bootstrap of Efron does not appear to be a natural alternative, as it relies on resamples which contain ties. The aim of this work is to investigate the use of subsampling in the aforementioned framework. The latter consists of basing the inference on statistic values computed from subsamples of the initial data. One of its advantages in the rank-based context under consideration is that the formed subsamples do not contain ties. Another advantage is its asymptotic validity under minimalistic conditions. In this work, we show the asymptotic validity of subsampling for several (weighted, smooth) empirical copula processes both in the case of serially independent observations and time series. In the former case, subsampling is observed to be substantially better than the empirical bootstrap and equivalent, overall, to the multiplier bootstrap in terms of finite-sample performance.

翻译：在模拟连续的多变量分布时,对未知的千兆字节进行推断的一个关键工具是非参数性估计,称为经验性千兆字节。一种常见的抽样分布方式是使用乘数靴。但后者的特点是执行成本高。鉴于经验性千兆字节的等级性质,古典经验性靴带似乎不是一个自然的替代方法,因为它依赖于含有关联的再抽样。这项工作的目的是调查上述框架中次级抽样的使用情况。后者包括从初始数据子抽样中计算统计值的推断。在所考虑的以等级为基础的背景中,其优点之一是所形成的子样本并不包含关联。另一个优点是在最低条件下,它具有无症状的有效性。在这项工作中,我们展示了子抽样(加权的、平滑的)实证性,在上述框架中,对子取样过程的使用情况进行调查。后者包括从初始数据的子样本中计算得出的统计值的基数。在所考虑的基于等级的背景中,其优点之一是,在所形成的子样本中并不包含任何联系。在最低条件下,我们所观察到的是,在一系列独立观测和时间序列中,在前的底层一级,对等的容器中,比等的测得更精确的测得。