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Various goodness-of-fit tests are designed based on the so-called informationmatrix equivalence: if the assumed model is correctly specified, twoinformation matrices that are derived from the likelihood function areequivalent. In the literature, this principle has been established for thelikelihood function with fully observed data, but it has not been verifiedunder the likelihood for censored data. In this manuscript, we prove theinformation matrix equivalence in the framework of semiparametric copula modelsfor multivariate censored survival data. Based on this equivalence, we proposean information ratio (IR) test for the specification of the copula function.The IR statistic is constructed via comparing consistent estimates of the twoinformation matrices. We derive the asymptotic distribution of the IR statisticand propose a parametric bootstrap procedure for the finite-sample $P$-valuecalculation. The performance of the IR test is investigated via a simulationstudy and a real data example.

Information matrix equivalence in the presence of censoring: A goodness-of-fit test for semiparametric copula models with multivariate survival data