Local Power Analyses of Goodness-of-fit Tests for Copulas

The asymptotic behaviour of several goodness-of-fit statistics for copula families is obtained under contiguous alternatives. Many comparisons between a Cramér-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 Cramér-von Mises test and that some of the moment-based statistics can provide simple and efficient goodness-of-fit methods. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.