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.
