CAREER: Nonparametric likelihood, estimating functions, and causal inference

Fisher提出的似然估计是统计学中的一个中心概念，无论从频率论还是贝叶斯的观点来看。该研究项目是推进一个非参数似然方法，既保留了原来的意义和Fisher的似然推理能力，并在同一时间构造面向点估计和Wald型置信区间的估计函数。研究了在缺失数据存在和不存在的情况下，两样本回归问题的半参数模型。该项目还调查了在具有时间依赖性治疗和混杂因素的纵向研究中用于因果推断的统计工具。调查员的教育计划包括设计一门关于非参数似然和估计函数的课程，并将其应用于半参数模型和因果推理;指导具有各种背景的学生;建立一个因果推理工作组，作为研究和教育平台;以及为研究人员和学生举办因果推理工作坊，以促进沟通和合作。这项研究将提高在环境、生物医学和社会经济研究中，对环境暴露、医疗、行为干预等进行推断。教育活动将帮助来自不同背景的学生和来自不同学科的研究人员获得最先进的统计思想和方法进行实证调查和发现。

Likelihood introduced by Fisher is a central concept in statistics both from frequentist and Bayesian viewpoints. The research project is to advance a nonparametric likelihood approach that retains both the original meaning and the inferential power of Fisher's likelihood, and at the same time to construct estimating functions geared towards point estimators and Wald-type confidence intervals. The research studies semiparametric models for two-sample and regression problems in the absence and in the presence of missing data. The project also investigates statistical tools for causal inference in longitudinal studies with time-dependent treatments and confounders. The investigator's education plan involves designing a course on nonparametric likelihood and estimating functions with applications to semiparametric models and causal inference; supervising students with various backgrounds; establishing a causal inference working group as a research and educational platform; and organizing causal inference workshops for researchers and students to facilitate communications and collaborations.The research will improve the validity and accuracy of inferences about environmental exposures, medical treatments, behavioral interventions among others in environmental, biomedical, and socioeconomic studies. The educational activities will help students from various backgrounds and researchers from various disciplines to acquire state-of-the-art statistical ideas and methods for empirical investigation and discovery.