Bootstrapping L 2 -type statistics in copula density testing

Summary In this paper, we address the problem of testing the goodness of fit of a copula density function in the context of a d -dimensional i.i.d. sample by using a L 2 -type statistic. In extension to Fermanian [4], we propose to use a bootstrap approximation of the distribution of the test statistic. We show the validity of the bootstrap and perform a simulation study. Stochastic independence can be characterised in terms of the underlying copula and so we use the test as a test of independence.