Some parametric and semiparametric inference in survival analysis and reliability

生存分析和可靠性中的一些参数和半参数推理

• 批准号: RGPIN-2015-05211
• 负责人: Balakrishnan, Narayanaswamy
• 金额: $ 2.26万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=613416
• 关键词: Some; parametric; semiparametric; inference; survival

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.

在过去的6年中，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上。我计划在所有这些领域中提出一些出色的问题。 生存分析：通过假设复发事件的计数过程为非均匀的泊松过程，已经在面板数数据分析和有效的非参数测试上完成了许多工作。但是，泊松过程是一个相当限制的模型，因为它被等级了，我建议通过假设加权泊松过程为重复事件进行加权泊松过程，以捕获权重函数以捕获过度和不足的分散。 已经研究了许多灵活的治疗速率模型和相关的参数推断。我建议通过比例危害模型在半参数设置中开发固化速率模型，然后在基线危害函数的参数和非参数形式下开发推论方法。 可靠性分析：已经研究了针对不同终生分布的一声设备测试数据的可能性推断。我计划将这项工作扩展到两个方向：开发半参数推断，并考虑竞争原因场景并开发相关的推论方法。我还计划根据先验信息开发最佳测试设计。 Wiener和Gamma退化模型已经完成了许多工作。但是，没有在制定因某些退化过程监控失败监控的单位的验收抽样计划方面做出的工作，我计划在此问题上进行工作，并开发样本量确定方法，这些方法对可靠性工程师有用。 有序的数据分析：签名概念可以对连贯的可靠性系统进行系统的研究。最近，鉴于n个系统的有序故障时间，基于系统的条件故障概率引入了有序签名。我想探索它们在开发可能性推断的可能性，尤其是有效的EM-Algorithms中的用途，以及基于系统寿命数据的某些生命周期参数（例如分位数，可靠性和累积危害）的确切非参数推断。 分布理论：在文献中引入了几种新的多元偏斜分布，并且已经研究了它们的偏度属性和测试。我计划对多元峰度措施以及峰度测试进行类似的详细研究，尤其是用于测试多元正态性。 对该领域和加拿大的预期成果和益处：我所监督的大多数后DOC和博士生都在世界各地的许多机构中担任了加拿大卡尔加里，曼尼托巴省和麦克马斯特的职位。其他一些人也加入了加拿大公司，例如Bombardier，BMO，CIBC，RBC，GE Capital和Rogers。我预计提议的工作会带来类似的好处。