Analysis of Absolute Deviation, Inference and Model Selection

该项目为某些回归模型开发了一种估计、模型选择和推断的综合方法，并将其应用于卫生科学、经济学、天文学以及其他科学调查学科。该项目的各个部分通过几个关键部分联系在一起：计算方面通过线性规划处理，推理通过基于模拟的重采样进行，同时估计和模型选择通过适当构造的惩罚函数进行，渐近性质通过经验过程理论进行。研究人员开发了参数估计和分布逼近的有效算法，建立了小样本和大样本的性质，并将方法和理论扩展到具有删失、截断或其他类型的非随机性的数据。本研究项目是由许多重要的科学学科领域推动的，并与之密切相关，包括健康和生命科学、经济学、天文学和社会学。它开发了新的工具，以评估健康风险、药物和治疗效果以及遗传变异，分析政策形成，如对失业和医疗保险的干预，以及了解天文现象。它为吸引和培训学生提供了一个平台，提供了多学科应用的工具。

This project develops a comprehensive approach to estimation,model selection and inferences for certain regression models, withapplications to health sciences, economics, astronomy as well asother disciplines of scientific investigations. Various parts ofthe project are connected through several key components:computational aspect is handled by linear programming, inferencesby simulation-based resampling, simultaneous estimation and modelselection by suitably constructed penalty functions, andasymptotic properties by empirical process theory. Theinvestigator develops efficient algorithms for parameterestimation and distributional approximation, establishes small andlarge sample properties, and extends the methods and theory todata with censoring, truncation or other kind of non-randommissingness.This research project is motivated by and closely related to manyimportant areas of scientific disciplines, including health andlife sciences, economics, astronomy and sociology. It develops newtools to assess health risks, drugs and treatments effects andgenetic variations, to analyze policy formation, such asintervention in unemployment and health insurance, as well as tounderstand astronomical phenomena. It provides a platform toattract and train students with tools for multi-disciplinaryapplications.