Multiple decrement modeling in various censoring and masking contexts

该研究计划的范围是创新的，实用的，并在其应用深远。该程序的主要目的是推广B的单变量生存函数的经典自洽非参数极大似然估计（NPMLE）。特恩布尔（康奈尔）到高原的多次递减。此外，在新提出的模型中，将保留掩蔽的可能性（其中一些可能的失效模式可以作为特定观察的潜在候选者被排除）和删失的存在（其中失效时间没有被精确观察到）。与迄今为止文献中发现的任何先前模型不同，将开发的迭代算法将完全由数据驱动且无分布，具有足够的灵活性以处理任何掩蔽失效模式的组合。这些算法提供了每个竞争风险的累积发生率函数或相关的单一风险生存函数的估计。此外，在研究计划的每个步骤中，将对模型进行许多增强。除了开发可以在许多不同的删失和掩蔽方案（如区间截断数据、信息掩蔽等）存在的情况下发挥作用的模型外，以及不同的模型假设（例如相关竞争风险），还将对模型进行核心修改。借鉴W.J. Braun（西方）、T. Duschesne（拉瓦尔）和J.斯塔福德（多伦多）在单变量环境中进行的，广义算法将在一系列方面得到增强，最显著的是在收敛性、准确性和效率方面。简而言之，这项研究的结果将在精算学以及任何其他遇到多重递减失败的领域（如生物统计学或工程学）中得到广泛应用。

The scope of this research program is innovative, practical, and far-reaching in its application. The primary thrust of the program is to generalize the classic self-consistent and nonparametric maximum likelihood estimators (NPMLE's) of the univariate survival functions of B. Turnbull (Cornell) to the plateau of multiple decrements. In addition, the possibility of masking (where some of the possible failure modes can be eliminated as potential candidates for a particular observation) and the presence of censoring (where the time-to-failure is not observed exactly) will be retained in the new proposed models. The iterative algorithms that will be developed, unlike any previous models found in the literature to date, will be exclusively data-driven and distribution-free, being flexible enough to handle any combination of masked failure modes. These algorithms provide estimators of either the cumulative incidence functions for each competing risk or the associated single risk survival functions. Furthermore, there will be many enhancements made to the models at each step of the research program. Apart from developing models that can function in the presence of many diverse censoring and masking schemes (such as interval-truncated data, informative masking, etc.), as well as different model assumptions (such as dependent competing risks), a kernel modification to the models will also be implemented. Drawing on the work of W.J. Braun (Western), T. Duschesne (Laval), and J. Stafford (Toronto) conducted in a univariate setting, the generalized algorithms will be enhanced in a litany of ways, most notably in the areas of convergence, accuracy, and efficiency. In short, the results from this research will find generous application in actuarial science, as well as any other field that encounters multiple decrement failures, such as biostatistics or engineering.