Mathematical Sciences: Bootstrap Asymptotics, Stochastic Differential Equations and Optimal Control, and Non- parametric Estimation for Diffusion Processes

首席研究员将继续研究Bootstrap方法中重采样样本的概率特性。这一研究将扩展到Bootstapping随机过程，如布朗运动。我们将探讨更改重采样大小的效果。从调整后的经验分布而不是原始经验分布进行重采样将被证明是更好的。我们将找到U统计量的自举极限定理。对自举现象的概率研究不仅得到了一些有趣的概率定理，而且得到了更好的自举方法，并证明了已有方法的有效性。

The principal investigator will continue his study of the probabilistic properties of the resampled sample in the bootstrap methods. The investigation will extend to bootstraping stochastic processes such as Brownian motion. The effects of changing the resampling size will be explored. Resampling from a trimmed empirical rather than the original empirical distribution will be shown to be better. Limit theorems for bootstraping of the U statistics will be found. The probabilistic study of the bootstraping phenomena leads to not only interesting theorems in probability but better bootstraping methods and the validity for the existing methods.