Theory and Applications of U-statistics for Multistate Models under Censoring

u型统计是统计学理论和方法中的基本对象。它们是样本均值的概括，直接或间接地涵盖了整个估计量范围，估计函数（对于参数的每个值）和检验统计量。本提案的目的是在一个统一的框架下，系统地研究一类可能出现在各种多状态审查数据问题中的统计数据。多状态模型是渐进系统，其中个体从一种状态移动到另一种状态，结果数据是事件时间数据的概括。感兴趣的变量包括各种转换时间、到达和离开给定状态的进入和存在时间、给定暂态中的等待时间等等，或者是上述所有变量和附加协变量（如果有的话）的混合。考虑了右截尾和间隔截尾的多态数据。研究了u统计理论和方法在多状态问题非参数检验和置信区间构造中的应用。多状态数据出现在不同的领域和应用中。例如，各州可根据病人的健康状况、住房市场的强弱或世界各地的气候条件等作出相应的规定。因此，预计所得方法将为包括医学、市场营销、政治学和工程学在内的多个学科的研究人员提供有价值的统计工具。拟议的研究也将大大有助于培训未来的统计人员，因为其中一部分将在PI的监督下用于博士论文，一些研究结果将纳入研究生课程。

U-statistics are fundamental objects in the theory and methods of statistics. They are generalizations of sample means and cover directly or indirectly a whole range of estimators, estimating functions (for each value of the parameter) and test statistics. The purpose of this proposal is to investigate systematically a class of these statistics that may arise in various multistate censored data problems under a unified framework. Multistate models are progressive systems where individuals move from one state to the next and the resulting data are generalizations of event time data. The variables of interest include various transition times, entry and exist times to and from a given state, waiting times in a given transient state and so on or a mixture of all of the above and additional covariates, if any. Both right and interval censored multistate data are considered. Applications of the U-statistics theory and methods to the construction of nonparametric tests and confidence intervals in multistate problems are also studied. Multistate data arise in diverse fields and applications. For example, the states may correspond to the health status of patients or the strength of the housing market or the climatic conditions in various parts of the world and so on. As a result, it is expected that the resulting methods will provide valuable statistical tools to researchers in multiple disciplines including medicine, marketing, political science and engineering. The proposed research will also contribute substantially in training future statisticians since parts of it will be used for doctoral dissertations under PI's supervision and some of the findings will be incorporated in graduate level courses.