Goodness-of-fit test for semiparametric copula models with bivariate interval-censored data

This paper discusses the goodness-of-fit test of semiparametric copula models when one faces bivariate interval-censored failure time data, which often occur in many areas including epidemiological and medical studies as well as social science experiments. For the problem, three test statistics or procedures are proposed: two based on the pseudo in-and-out-sample approach and one based on the information ratio criterion. The asymptotic properties of the proposed test procedures are established, and in particular, the three methods are shown to be asymptotically equivalent. To assess the empirical performance of the proposed methods, an extensive simulation study is conducted and indicates that they work well in practical situations. An application to a Signal-Tandmobiel study is provided.