Actuarial Modeling of Competing Risks Under Various Dependence Structures

考虑到NSERC的主要目标是支持“正在进行的研究项目（具有长期目标），而不是单个短期项目或项目集合”，这项拨款提案旨在建立在一个已经存在的创新研究项目的基础上，该项目能够对精算和统计学科做出重大的额外贡献——不仅在学术文献中，而且在精算师、统计学家和其他人的日常工作中。到目前为止，我的主要研究领域集中在开发一类完全非参数算法，我称之为自一致竞争风险（SC-CR）算法，作为对故障时间分布建模的一种方法。******根据我到目前为止完成的研究计划的总体轨迹，目前的提案，代表了该计划的下一阶段，主要是为了将统计依赖性的维度纳入SC-CR算法。尽管迄今为止我们提出的模型在精算师和其他人遇到的许多情况下都有充分的应用，但在实践中，它们确实倾向于严重依赖于统计独立性的假设。为了更实际地使用，独立性假设（通常是一个非常强大的假设）将需要放松。依赖性可以表现为许多不同的方式：依赖掩蔽、依赖滤波、掩蔽与滤波之间的依赖、减量之间的依赖等。将考虑不同的建模依赖方法，最值得注意的是使用copula理论。我们将有意识地努力使关联函数的估计量保持非参数，或者尽可能地接近于此。简而言之，在本研究项目中开发的模型通过提供能够对竞争风险数据建模的非参数模型，同时允许可能性审查、屏蔽和依赖性，解决了文献中的一个重要空白。******随着这些依赖模型的理论结果的出现，大量的统计模拟将得到保证。统计属性，如一致性（不要与上面提到的自一致性属性混淆）、非参数最大似然性和无偏性都应该进行验证。我特别计划利用硕士生的帮助来执行研究项目的各个计算方面，就像我过去所做的那样，作为进一步推进HQP培训的一种方式。此外，由于大多数编程预计将使用统计软件R来实现，因此也有可能创建和/或贡献一个R统计包，供从业者使用。随着每个依赖模型的开发，以及估算器的统计属性的建立，结果可以传播到更广泛的精算和统计社区。＊＊＊＊＊

Mindful of NSERC's principle aim of supporting, "ongoing programs of research (with long-term goals) rather than a single short-term project or collection of projects", this grant proposal is designed to build upon an already existing innovative research program that is capable of significant additional contributions to the actuarial and statistical disciplines --- not only in the academic literature, but also in the day-to-day work of actuaries, statisticians, and others. To date, my main area of research has centered on developing a whole class of fully nonparametric algorithms, which I have called Self-Consistent Competing Risks (SC-CR) Algorithms, as a way to model failure time distributions. ******Following the overall trajectory of my research program accomplished so far, the current proposal, representing the next phase in the program, is primarily designed to incorporate the dimension of statistical dependence into the SC-CR Algorithms. Although the models we have proposed to date have ample application to many circumstances encountered by actuaries and others, in practice they do tend to rely heavily on the assumption of statistical independence. To be of even more practical use then, the independence assumption, which is often a very strong assumption, will need to be relaxed. Dependence can be manifested in many different ways: dependent masking, dependent censoring, dependence between masking and censoring, dependence between decrements, etc. Different approaches to modeling dependence will be considered, most notably with the use of copula theory. A conscious effort will be made to keep the estimators of the incidence functions nonparametric, or as close to this as possible. In short, the models that will be developed in this research program address a significant void in the literature by providing nonparametric models capable of modeling competing risks data while allowing for the possibility censoring, masking, and dependence.******As the theoretical results of each of these dependence models emerges, a significant amount of statistical simulation will be warranted. Statistical attributes such as consistency (not to be confused with the property of self-consistency mentioned above), nonparametric maximum likelihood, and unbiasedness should all be verified. I especially plan to utilize the aid of Master's students to execute various computational aspects of the research program, as I have done in the past, as a way to further advance HQP training. Furthermore, since most of the programming is anticipated to be implemented with the statistical software R, there is also the possibility of creating, and/or contributing to, an R statistical package that can then be used by practitioners. As each of the dependence models are developed, and the statistical attributes of the estimators established, the results can then be disseminated to the wider actuarial and statistical communities. *****