Asymptotics of empirical copula processes under nonrestrictive smoothness assumptions

Details Asymptotics of empirical copula processes under nonrestrictive smoothness assumptions Asymptotics of empirical copula processes under nonrestrictive smoothness assumptions

2010-12-09

arxiv.org/abs/1012.2133v2

Mathematics

Statistics Theory

22 pages

Scientific paper

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 nonrestrictive in the sense that it is needed anyway to ensure the candidate limiting process to exist and have 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.

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