Mathematical Sciences: Asymptotic Behavior of Dependent Sequences of Random Variables and Applications

数学科学：随机变量相关序列的渐近行为及其应用

• 批准号: 9304010
• 负责人: Magda Peligrad
• 金额: $ 6万
• 依托单位: University of Cincinnati Main Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304010&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Asymptotic; Behavior; Dependent

This research involves the investigation of the asymptotic properties of sequences of random variables with various types of dependence. By relating weak dependent sequences to semiamarts and demimartingales we shall clarify some aspects of the almost sure convergence of these sequences. Other part of this research will study two estimators of the variance of the sample mean based on dependent data. These estimators are suggested by blocking techniques and robust statistical procedures such as the bootstrap and the jackknife. The estimators can be used as selfnormalizers in the Central Limit Theorem. One of the main problems of statistics is to provide interval estimates for some unknown parameters. These confidence intervals are constructed based on an estimator of the parameter and an error given by the variability of this estimator. The purpose of this research is to study this problem in the case when the data is dependent.

本文研究了具有不同相依关系的随机变量序列的渐近性质。通过将弱相依序列与半序和半序序联系起来，我们将阐明这些序列几乎必然收敛的某些方面。本研究的其他部分将研究基于相依数据的样本均值的方差的两个估计量。这些估计器是通过分块技术和稳健的统计程序(如Bootstrap和jacksave)建议的。这些估计量可用作中心极限定理中的自归一化函数。统计学的主要问题之一是给出一些未知参数的区间估计。这些可信区间是基于参数的估计器和该估计器的可变性所给出的误差来构造的。本研究的目的是在数据相依的情况下研究这一问题。