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

翻译：多种拟合优度检验基于所谓的信息矩阵等价性设计：若所假设模型正确指定，则源于似然函数的两个信息矩阵等价。文献中，该原理已针对完全观测数据的似然函数建立，但尚未在删失数据似然下得到验证。本文证明了多变量删失生存数据半参数Copula模型框架下的信息矩阵等价性。基于此等价性，我们提出用于检验Copula函数设定正确性的信息比检验。通过比较两个信息矩阵的一致估计量构建信息比统计量，推导其渐近分布，并提出了有限样本下计算$P$值的参数自助法。通过模拟研究与真实数据案例考察了信息比检验的性能。