Mathematical Sciences: Topics in Multivariate Survival Analysis and Counting Processes

建议： DMS 9504507 PI：Dorota Dabrowska机构：UCLA职务： 多变量生存分析和计数过程主题 摘要： 本研究的目的是扩展多参数乘积积分和平滑技术在生存分析中的应用。基于平滑积积分的密度和非参数回归的渐近性质将被开发用于以下方面：独立于删失数据的秩检验的数据自适应构造;来自截断数据的多变量生存函数的非参数估计;脆弱模型中的拟合优度;以及线性变换模型中的分位数导数回归。研究结果将应用于艾滋病和双胞胎研究的数据分析。 多变量生存分析是一个快速发展的领域，在遗传流行病学、天文学、计量经济学等领域有着广泛的应用。本研究的目的是开发统计方法，分析这些研究中产生的数据。

Proposal: DMS 9504507 PI: Dorota Dabrowska Institution: UCLA Title: Topics in multivariate survival analysis and counting processes Abstract: The objective of this research is to extend applications of multiparameter product integrals and smoothing techniques in survival analysis. Asymptotic properties of density and nonparametric regression based on smoothed product integrals will be developed for the following: data adaptive construction of rank tests for independence from censored data; nonparametric estimation of multivariate survival functions from truncated data; goodness-of-fit in frailty models; and quantile derivative regression in linear transformation models. The results will be applied to the analysis of data from AIDS and twin studies. Multivariate survival analysis is a rapidly growing area with a wide range of applications in genetic epidemiology, astronomy, econometrics and other fields. The aim of this research is to develop statistical methods for analysis of data arising in such studies.