Mathematical Sciences: Statistical Inference for Markov Chains and Regression Models: Estimation, Bootstrapping and Related Asymptotics

数学科学：马尔可夫链和回归模型的统计推断：估计、自举和相关渐近学

• 批准号: 9007182
• 负责人: Krishna Athreya
• 金额: $ 1.51万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007182&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Inference; Markov

The method of resampling for statistical inference known as the "bootstrap" has proved useful in situations where the data are observations from independent identically distributed random variables and this research will extend the method to a simple kind of dependence encountered in the Markov chain. One case that will be considered is that of a Markov chain with a countable state space and homogeneous transition probabilities. The question of whether or not it is possible to provide bootstrap descriptions of the distribution of the difference of the empirical and true transition probabilities will be examined. Related questions for the estimation of the distribution of hitting times, stationary distributions, etc., for recurrent Markov chains with finite, countable and uncountable state spaces will be studied.

用于统计推断的方法称为 “引导”已经证明在数据 是独立同分布随机 变量，本研究将方法扩展到一个简单的 这是马尔可夫链中的一种依赖关系。的一个案件 将被认为是一个马尔可夫链与可数 状态空间和齐次转移概率。的 是否有可能提供引导的问题 的差异分布的描述 将检验经验和真实的转移概率。 关于估计分布的有关问题 命中时间、平稳分布等，治疗复发性 有限、可数和不可数状态空间的马尔可夫链 将被研究。