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 |U ≤ α) for α ϵ (o,1] every . 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.