Local modeling for multivariate extremes and survival analysis

多元极端值和生存分析的局部建模

• 批准号: 110482-2009
• 负责人: Abdous, Belkacem
• 金额: $ 1.82万
• 依托单位: Université Laval
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=569160
• 关键词: Local; modeling; multivariate; extremes; survival

The general objective of the proposed research program is to use and adapt local modeling methods in various class of non-parametric models. Theoretical and practical aspects of the obtained estimators will be investigated. In particular, we shall focus on the following estimation problems: 1. Extreme values related problems: In many applied problems, one needs to quantify the asymptotic dependence structure of multivariate data in order to estimate probabilities of associated rare sets. Our aim in this project is to investigate local modeling techniques when applied to the estimation of copulas, dependence functions, multivariate tail dependence measures, conditional probabilities associated to a random vector whose components are not necessarily jointly extreme. We also intend to use tail dependence measures and classical correlation coefficients to test independence of multivariate extremes. 2. Survival analysis: Analysis of time-to-event data is a problem frequently faced in various fields: medicine, public health, epidemiology, engineering, etc. There is a huge literature on this subject. Our scope for this project is to investigate local modeling for survival functions, regression, mean residual life functions, regression quantiles and various risk measures when : a) the lifetime and the censoring (or truncating) time are univariate dependent variables. or b) the observed lifetimes are bivariate (or multivariate) variables with unique or different censoring variables. 3. Item Response Theory and Equipercentile Equating are two different topics that we intend to investigate by using local fitting. They are related to Health Quality of Life, questionnaires and instruments used in health science.

所提出的研究计划的总体目标是在各种类型的非参数模型中使用和适应局部建模方法。将对所获得的估计器进行理论和实践方面的研究。 特别是，我们将重点解决以下估计问题： 1.极值相关问题：在许多应用问题中，为了估计相关稀有集的概率，需要量化多变量数据的渐近依赖结构。我们在这个项目中的目的是研究局部建模技术，当应用于Copula、相关性函数、多变量尾部相关性度量、与其分量不一定是联合极值的随机向量相关的条件概率的估计时。我们还打算使用尾部相关性度量和经典相关系数来检验多变量极值的独立性。 2.生存分析：事件发生时间数据的分析是医学、公共卫生、流行病学、工程学等各个领域经常面临的问题。我们这个项目的范围是调查生存函数、回归、平均剩余寿命函数、回归分位数和各种风险度量的局部建模，在以下情况下： A)寿命和截尾(或截尾)时间是单变量因变量。 或 B)观察到的寿命是具有唯一或不同截尾变量的二元(或多元)变量。 3.项目反应理论和等百分位等值是两个不同的主题，我们打算用局部拟合法来研究。它们与健康生活质量、健康科学中使用的问卷和工具有关。