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.
