CAREER: Nonparametric likelihood, estimating functions, and causal inference

从频数和贝叶斯的角度来看，Fisher引入的似然都是统计学中的一个核心概念。研究项目是提出一种非参数似然方法，它既保留了Fisher似然的原始含义和推理能力，又构造了向着点估计和Wald-型可信区间的估计函数。研究了两样本半参数模型和缺失数据条件下的回归问题。该项目还调查了在纵向研究中使用统计工具进行因果推断的情况，这些研究的处理方法和混杂因素与时间相关。研究人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；指导不同背景的学生；建立因果推理工作组作为研究和教育平台；为研究人员和学生组织因果推理研讨会，以促进交流和合作。该研究将提高环境暴露、医疗、行为干预等环境、生物医学和社会经济学研究中的推理的有效性和准确性。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新的统计思想和方法，用于实证调查和发现。

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.