Limit Theorems for Various Dependence Structures with Applications to Statistics and Particle Systems

9803625Rinott本研究的重点是随机变量的相关结构和相关的大样本分布。 结果预计包括单变量和多元正态近似，中心极限定理和系列扩展的分布依赖和。 这样的结果将扩展经典理论，假设独立，并允许许多新的应用在统计学，组合学和计算机科学，其中一个处理的总和和计数的因变量。 斯坦的方法在提案中发挥了重要作用，但其他方法也有特色。 一个仔细的研究的收敛速度。该建议描述了博弈论、大样本理论、统计力学中的粒子系统等的应用。大型粒子系统、大型统计调查、大型计算系统等的概率行为，通常通过考虑系统大小的限制来研究，并假设粒子的独立性，或调查的意见等。然而，对于许多系统或抽样方案，随机结果之间的相关性不能忽略。 本研究集中于研究存在依赖的大型系统或样本的方法，以及在各种依赖结构下。 研究了有限系统接近其极限行为的速率，从而将结果应用于给定有限尺寸的系统。

9803625RinottThis research focuses on dependence structures of random variables and associated large sample distributions. Results are expected to include univariate and multivariate normal approximations, Central Limit Theorems and series expansions of distributions for dependent summands. Such results will extend the classical theory, which assumes independence, and allow many new applications in statistics, combinatorics and computer science, where one deals with sums and counts of dependent variables. Stein's methods play an important role in the proposal, but other methods are featured as well. A careful study of convergence rates is proposed. Applications to game theory, large sample theory, particle systems in statistical mechanics and others, are described in the proposal.The probabilistic behavior of large systems of particles, large statistical surveys, large computational systems, etc., is often studied by considering limits as the size of the system grows, and assuming independence of the particles, or opinions surveyed etc. However, for many systems or sampling schemes, the dependence between the random outcomes cannot be ignored. This research concentrates on methods of studying large systems or samples in the presence of dependence, and under various dependence structures. The rate at which finite systems approach their limiting behavior is studied, thus allowing applications of the results to systems of a given finite size.