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

这项研究将包括两个主要的主题，数据被测量误差破坏时的推断问题和随机变量的鞅类型序列的不等式。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。要研究的推理方法包括基于近似数据模型的最大似然、条件似然和拟似然估计。第二个主题涉及到的比较方法的正切序列的鞅差异。我们将特别关注具有条件独立增量的鞅所控制的问题。要研究的具体主题包括模不等式性、指数不等式性和鞅类型序列的稳定性性质。这项研究集中在两个不同的主题上。第一个领域涉及不精确测量数据时的推断和数据分析问题。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。

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.