Mathematical Sciences: Self-Normalization and Empirical CLT's

首席研究员将对三个 与渐近分布理论有关的问题 独立同分布随机变量的和。 第一个问题是完全确定渐近 中间体的学生化版本的分布， 对称分布的幅度截尾和。 第二 问题是根据经验重建一个和的分布， 中等长度。 提出了仿射重建， 通过中心，尺度和仿射归一化的近似， 依法 第三个问题是研究一个位置不变量 方法的大小审查总和，利用新的 由校长开发的定心和缩放技术 调查员 首席研究员将对三个 与渐近分布理论有关的问题 独立同分布随机变量的和。 这一研究领域，极限理论，是许多 经典概率 这一领域的问题已经激发了 从统计数据来看。

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.