Mathematical Sciences: Quantile-Uniform Empirical Distribution Function Methods in Probability Theory

点击翻译按钮获取中文摘要

The principal investigator will continue his work in probability theory in the area of empirical processes. Essential to his quantile-uniform empirical distribution function approach is the study of the large sample properties of the uniform empirical process and their relationship through the probability integral transformation to those of arbitrary real valued random variables. He will consider problems on the studies of limit results for sums of intermediate extreme values and records, functional laws of the iterated logarithm for increment processes and a notion of generalized quantiles. The principal investigator will continue his work in probability theory in the area of empirical processes. Empirical processes theory has largely been concerned with uniform analogues of the classical limit theorems for sums of independent random variables, which is the foundations of mathematical statistics. The investigator will continue to develope an approach he developed to study limit theorems for intermediate extreme values.