Local sensitivity analyses of goodness-of-fit tests for copulas

Abstract

The asymptotic behavior of several goodness-of-fit statistics for copula families is obtained under contiguous alternatives. Many comparisons between a Craméer-von Mises functional of the empirical copula process and new moment-based goodness-of-fit statistics are made by considering their associated asymptotic local power curves. It is shown that the choice of the estimator for the unknown parameter can have a significant influence on the power of the Craméer-von Mises test, and that some of the moment-based statistics can provide simple and efficient goodness-of-fit methods. The paper ends with an extensive simulation study that aims to extend the conclusions to small and moderate sample sizes.