Mathematical Sciences: Topics in Multivariate Survival Analysis and Counting Processes

建议：DMS 9504507 PI：Dorota Dabrowska研究所：加州大学洛杉矶分校标题：多元生存分析和计数过程主题摘要：本研究的目的是扩大多参数乘积积分和平滑技术在生存分析中的应用。基于光滑积积分的密度和非参数回归的渐近性质将被发展为：数据自适应构造独立于删失数据的等级检验；从截断数据中非参数估计多变量生存函数；在脆弱模型中的拟合度；在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。多元生存分析是一个发展迅速的领域，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。这项研究的目的是开发统计方法来分析此类研究中产生的数据。

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.