A Test for Truncation Invariant Dependence.

A test is proposed to check whether a random sample comes from a truncation invariant copula C, that is, if C is the copula of a pair (U, V) of random variables uniformly distributed on [0, 1], then C is also the copula of the conditional distribution function of (U, V vertical bar U <= alpha) for every alpha epsilon (0, 1]. The asymptotic normality of the test statistics is shown. Moreover, a procedure is described to simplify the approximation of the asymptotic variance of the test. Its performance is investigated in a simulation study.