Asymptotics of empirical copula processes under non-restrictive smoothness assumptions
Asymptotics of empirical copula processes under non-restrictive smoothness assumptions
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DOI：
10.3150/11-bej387
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发表时间：
2012-08-01
期刊：
影响因子：
1.5
通讯作者：
Segers, Johan
中科院分区：
文献类型：
--
作者：
Segers, Johan
在假设Copula的一阶偏导数存在且在单位超立方体的某些子集上连续的假设下，证明了经验Copula过程的弱收敛.这个假设是非限制性的，因为无论如何都需要它来确保候选限制过程的存在和具有连续的轨迹。此外，基于乘子中心极限定理的重采样方法仍然有效，这些方法需要对一阶导数进行一致估计。在允许边界附近爆炸行为的二阶偏导数上的某些增长条件下，可以恢复经验Copula过程的Stute表示中的几乎必然的速率。例如，在相关矩阵为满秩高斯Copula、许多阿基米德Copula和许多极值Copula的情况下，验证了这些条件。
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is non-restrictive in the sense that it is needed anyway to ensure that the candidate limiting process exists and has continuous trajectories. In addition, resampling methods based on the multiplier central limit theorem, which require consistent estimation of the first-order derivatives, continue to be valid. Under certain growth conditions on the second-order partial derivatives that allow for explosive behavior near the boundaries, the almost sure rate in Stute's representation of the empirical copula process can be recovered. The conditions are verified, for instance, in the case of the Gaussian copula with full-rank correlation matrix, many Archimedean copulas, and many extreme-value copulas.