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.

在从独立分布的随机变量中观察数据的情况下，被称为“引导程序”的统计推断的重新采样方法已被证明是有用的，并且该研究将将该方法扩展到马尔可夫链中遇到的一种简单的依赖性。一种将要考虑的情况是马尔可夫链，具有可比状态空间和均匀过渡概率。是否可以检查是否可以对经验和真实过渡概率的差异分布进行自举描述的问题。 将研究具有有限，可数和无数状态空间的经常性马尔可夫链的打击时间，固定分布等分布的相关问题。