Mathematical Sciences: Self-Normalization and Empirical CLT's

主要研究人员将对与独立、同分布随机变量和的渐近分布理论相关的三个问题进行研究。第一个问题是完全确定对称分布的中间的、幅度修剪和的学生化形式的渐近分布。第二个问题是经验性地重建中间长度和的分布。通过中心、尺度和仿射归一化规律的逼近，提出了一种仿射重构方法。第三个问题是利用首席研究员开发的一种新的居中和缩放技术，研究一种位置不变的方法来审查总和。主要研究人员将对与独立、同分布随机变量和的渐近分布理论相关的三个问题进行研究。这一研究领域，即极限理论，是许多经典概率的核心。这一领域的问题是由统计数字引起的。

The principal investigator will conduct research on three problems connected with the theory of asymptotic distributions of sums of independent, identically distributed random variables. The first problem is to completely determine the asymptotic distribution of the studentized version of an intermediate, magnitude-trimmed sum for symmetric distributions. The second problem is to empirically reconstruct the distribution of a sum of intermediate length. An affine reconstruction is proposed, via center, scale, and an approximation to the affine-normalized law. The third problem is to investigate a location-invariant approach to magnitude-censoring for sums, utilizing a new centering and scaling technique developed by the principal investigator. The principal investigator will conduct research on three problems connected with the theory of asymptotic distributions of sums of independent, identically distributed random variables. This area of research, limit theory, is at the core of much of classical probability. Problems in this area have been motivated by statistics.