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

这项研究将涵盖两个主要课题，推理 数据因测量误差而损坏时的问题， 鞅型随机变量序列的不等式 第一个主题主要关注工具变量 广义线性和非线性测量误差估计 回归模型 研究的推理方法包括 最大似然、条件似然和拟似然 基于近似数据模型的估计。 第二主题 涉及鞅切序列的比较方法 差异 将特别注意问题 涉及鞅的控制 有条件的独立增量。 具体议题将 研究了范数不等式、指数不等式 鞅型序列的稳定性 这项研究集中在两个不同的主题。 的 第一个领域涉及推理和数据分析的问题， 数据没有被精确地测量。 第二个话题是关于 随机变量和的比较方法。 这些 方法提供了一个更好的理解现代概率 理论

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.