Mathematical Sciences: Statistics Inference in the Presence of Measurement Error: II

数学科学：存在测量误差的统计推断：II

• 批准号: 9200915
• 负责人: Leonard Stefanski
• 金额: $ 6.7万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-01 至 1995-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200915&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistics; Inference; Presence

This research will cover two major topics, inference problems when data are corrupted by errors of measurement and inequalities for martingale type sequences of random variables. The first topic focusses primarily on instrumental variable estimation in generalized linear and nonlinear measurement error regression models. Inference methods to be studied include maximum likelihood, conditional likelihood and quasilikelihood estimation based on approximate data models. The second topic involves comparison methods for tangent sequences of martingale differences. Special attention will be given to problems involving domination of martingales by martingales with conditionally independent increments. Specific topics to be investigated include norm inequalities, exponential inequalities and stability properties for martingale type sequences. This research is focussed on two different topics. The first area involves problems of inference and data analysis when data are not measured precisely. The second topic is concerned with comparison methods for sums of random variables. These methods provide a better understanding of modern probability theory.

本研究将涵盖两个主要的主题，即当数据被测量误差破坏时的推理问题和随机变量鞅型序列的不等式。第一个主题主要集中在广义线性和非线性测量误差回归模型中的工具变量估计。研究的推理方法包括基于近似数据模型的极大似然、条件似然和拟似然估计。第二个主题涉及鞅差切线序列的比较方法。将特别注意涉及鞅被具有条件独立增量的鞅支配的问题。要研究的具体主题包括范数不等式，指数不等式和鞅型序列的稳定性。这项研究集中在两个不同的主题上。第一个领域涉及数据测量不精确时的推理和数据分析问题。第二个主题是关于随机变量和的比较方法。这些方法有助于更好地理解现代概率论。