Some parametric and semiparametric inference in survival analysis and reliability

在过去的6年里，我的研究主要集中在生存分析、可靠性分析、有序数据分析和分布理论。我计划在所有这些方面都追求一些突出的问题。 生存分析：在面板计数数据分析方面已做了大量工作，并通过假设复发事件的计数过程为非齐次泊松过程而发展了有效的非参数检验。然而，Poisson过程是一个相当有限制性的模型，因为它是等离散度的，我建议对经常性事件假设一个加权泊松过程，并引入权函数来捕捉过度离散度和欠离散度。 人们已经研究了许多灵活的治愈率模型和相关的参数推断。我建议通过比例风险模型在半参数设置下建立治愈率模型，然后在基线风险函数的参数和非参数形式下开发推理方法。 可靠性分析：针对不同的寿命分布，研究了一次装置试验数据的似然推断。我计划在两个方向上扩展这项工作：发展半参数推理，考虑竞争原因情景，并开发相关的推理方法。我还计划根据先前的信息开发测试的优化设计。 在维纳和伽马退化模型方面已经做了很多工作。然而，对于通过某些退化过程监测其故障的机组，还没有关于制定验收抽样计划的工作，我计划解决这个问题，并开发对可靠性工程师有用的样本大小确定方法。 有序数据分析：签名的概念使系统研究连贯的可靠性系统成为可能。最近，基于给定n个系统的有序失效时间的系统的条件失效概率，引入了有序签名。我想探索它们在开发似然推理中的应用，特别是高效的EM算法，以及基于系统寿命数据对一些感兴趣的寿命参数(如分位数、可靠性和累积风险)进行精确的非参数推断。 分布理论：文献中介绍了几种新的多元偏态分布，并对它们的偏态性质和偏态检验进行了研究。我计划对多变量峰度度量以及峰度检验进行类似的详细研究，特别是对多变量正态分布的检验。 对实地和加拿大的预期结果和好处：我指导的大多数博士后和博士后都在世界各地的许多机构任职，包括加拿大的卡尔加里、马尼托巴省和麦克马斯特。其他一些公司加入了庞巴迪、蒙特利尔银行、加拿大帝国商业银行、加拿大皇家银行、通用电气资本和罗杰斯等加拿大公司。我预计拟议的工作将产生类似的好处。

During the past 6 years, my research has focused mainly on Survival Analysis, Reliability Analysis, Ordered Data Analysis and Distribution Theory. I plan to pursue some outstanding problems in all these areas. SURVIVAL ANALYSIS: Much work has been done on panel count data analysis and efficient nonparametric tests have been developed by assuming the counting process of the recurrent event to be a non-homogeneous Poisson process. However, Poisson process is quite a restrictive model as it is equi-dispersed and I propose to generalize by assuming a weighted Poisson process for the recurrent event incorporating weight functions to capture over- and under-dispersion. Many flexible cure rate models and associated parametric inference have been studied. I propose to develop cure rate models in a semi-parametric setup through a proportional hazards model and then develop inferential methods under parametric and nonparametric forms of the baseline hazard function. RELIABILITY ANALYSIS: Likelihood inference for one-shot device test data has been studied for different lifetime distributions. I plan to extend this work in two directions: to develop semi-parametric inference and to consider competing-cause scenario and develop associated inferential methods. I also plan to develop optimal design of tests based on prior information. Much work has been done on Wiener and gamma degradation models. However, no work has been done on the development of acceptance sampling plans for units whose failures are monitored by some degradation process, and I plan to work on this issue and also develop sample size determination methods that will be useful for reliability engineers. ORDERED DATA ANALYSIS: The notion of signatures enables a systematic study of coherent reliability systems. Recently, ordered signatures have been introduced based on conditional failure probabilities of systems given the ordered failure times of n systems. I want to explore their use in developing likelihood inference, especially efficient EM-algorithms, as well as exact nonparametric inference for some lifetime parameters of interest, such as quantile, reliability and cumulative hazard, based on system lifetime data. DISTRIBUTION THEORY: Several new multivariate skewed distributions have been introduced in the literature and their skewness properties and tests for skewness have been studied. I plan to carry out a similar detailed study of multivariate kurtosis measures as well as tests for kurtosis, especially for testing multivariate normality. Anticipated Outcomes and Benefits to the Field and to Canada: Most post-docs and PhD students I supervised have taken up positions in many institutions across the world, including Calgary, Manitoba and McMaster in Canada. Some others have joined Canadian companies such as Bombardier, BMO, CIBC, RBC, GE Capital and Rogers. I anticipate the proposed work to result in similar benefits.