Selected Large Sample Problems in Self-Normalized Sums, Generalized Extremes and Weighted Approximations

小行星9803344 概率论和统计学中的大样本问题关注的是 当样本大小增加到无穷大时，处理或统计。研究者计划 在三个自然出现这些问题的领域开展工作。具体如下：1. 自归一化和，2.广义极端，和3。加权近似 的 第一个领域的问题源于长期存在的问题， 经典学生t统计量的渐近分布。第二区的人来自 关于极值的极限分布问题，例如年最大值 气温、河高和人口中最高的收入。他概括了 的极端多变量设置，并建议研究其大样本特性。 最后，在第三部分，他打算研究近似有限样本的方法 通过渐近过程检验数据的相关性而产生的过程。这 应该提供一个有用的工具，以确定许多泛函的极限分布， 这样的有限采样过程。 解决所有三个研究领域的问题应该有许多 在统计推断和估计中的应用，特别是在多元和相关 在大样本可用的情况下。最终，希望许多人 结果将导致数据分析工具的建设，将进入 统计的日常实践。无论如何，他们应该提高我们对一个 有趣的随机行为

9803344 Mason Large sample problems in probability and statistics concern what happens to processes or statistics when the sample size increases to infinity. The investigator plans to work in three areas in which such problems naturally arise. These are the following: 1. self-normalized sums, 2. generalized extremes, and 3. weighted approximations. The problems in area 1 originate from the long standing question concerning the possible asymptotic distributions of the classical Student's t-statistic. Those in area 2 stem from questions about the limiting distribution of extreme values, such as annual maximum temperatures, river heights and largest incomes in a population. He generalizes the notion of extremes to a multivariate setting and proposes to study its large sample properties. Finally in area 3, he intends to look into methods of approximating finite sample processes that arise from testing for dependence in data by an asymptotic process. This should provide a useful tool to determine the limiting distribution of many functionals of such finite sample processes. Solutions to problems in all three areas of research should have numerous applications in statistical inference and estimation, especially in multivariate and dependent situations, whenever large samples are available. Eventually, it is hoped that many of the results will lead to the construction of data analytic tools which will enter into the everyday practice of statistics. In any case they should improve our understanding of an interesting range of random behavior.