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：根据所谓的信息矩阵等值设计了各种健康测试:如果假设模型得到正确指定,则根据概率函数得出的两个信息矩阵是等效的,在文献中,这项原则是用完全观察的数据确定概率功能的,但还没有根据审查数据的可能性加以核实。在本稿中,我们证明信息矩阵等值是多变量审查生存数据半参数相交模型框架内的信息矩阵等值。基于这一等值,我们提议对焦云函数的规格进行信息比(IR)测试。IR统计是通过比较两种信息矩阵的一致估计来构建的。我们得出IR统计的无特征分布,并提议对限定抽样的美元值计算采用参数性靴式程序。通过模拟研究和真实数据实例对IR测试的性能进行调查。