存在删失时的信息矩阵等价性：面向多变量生存数据的半参数copula模型拟合优度检验
Information matrix equivalence in the presence of censoring: A goodness-of-fit test for semiparametric copula models with multivariate survival data
AI总结：
该研究证明了多变量删失生存数据下半参数copula模型的信息矩阵等价性，提出基于该等价性的copula函数设定信息比检验，推导其渐近分布并给出有限样本P值计算的参数bootstrap程序，通过模拟与真实数据验证了检验性能。
摘要：
多种拟合优度检验均基于所谓的信息矩阵等价性设计：若假设的模型设定正确，则由似然函数推导得到的两个信息矩阵是等价的。现有文献中，该原理已在完全观测数据的似然函数下得到确立，但尚未在删失数据的似然函数下得到验证。本文在面向多变量删失生存数据的半参数copula模型框架下，证明了信息矩阵等价性。基于该等价性，我们提出了一种用于copula函数设定检验的信息比（IR）检验。IR统计量通过比较两个信息矩阵的一致估计量构建得到。我们推导了IR统计量的渐近分布，并提出了用于计算有限样本$P$值的参数bootstrap程序。我们通过模拟研究和真实数据示例探究了IR检验的性能。
英文摘要：
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.
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