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：在对连续多元分布进行建模时，推断未知联结函数的关键工具是称为经验联结函数的非参数估计量。近似其抽样分布的一种常用方法是乘子自助法，但该方法实施成本较高。鉴于经验联结函数基于秩的性质，Efron经典经验自助法因其重抽样样本包含结值而并非自然替代方案。本研究旨在探讨子抽样在上述框架中的应用——该方法基于初始数据子样本计算的统计量进行推断。在所考察的基于秩的背景下，其优势之一在于生成的子样本不含结值；另一优势是在极简条件下具有渐近有效性。本研究证明，对于多种（加权、平滑）经验联结函数过程，无论是独立观测序列情形还是时间序列情形，子抽样均具有渐近有效性。在独立观测情形下，子抽样的有限样本表现显著优于经验自助法，且总体与乘子自助法相当。