CAREER: Nonparametric likelihood, estimating functions, and causal inference

从频率论和贝叶斯的观点来看，费雪提出的似然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，既保留Fisher似然的原始意义，又保留Fisher似然的推理能力，同时构造面向点估计量和wald型置信区间的估计函数。研究了缺失数据和缺失数据情况下的双样本半参数模型和回归问题。该项目还调查了纵向研究中随时间变化的治疗和混杂因素的因果推理的统计工具。研究者的教育计划包括设计一门关于非参数似然和估计函数应用于半参数模型和因果推理的课程；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；并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。该研究将提高在环境、生物医学和社会经济研究中有关环境暴露、医学治疗、行为干预等方面推论的有效性和准确性。这些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，以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.