讲座主题：Statistical Inference for Mean Function of Longitudinal Imaging Data over Complicated Domains
主讲人：李杰
讲座时间：2021.4.28（周三）  10：15-11：15
地点：综合楼644
主讲人简介：  

Jie Li, a fourth-year Ph.D. candidate at Center for Statistical Science of Tsinghua University. His main research interest includes causal inference, time series, functional data analysis, and machine learning, as well as applications of statistics in environment, finance, medcine and meteorology. 

讲座摘要：

Motivated by longitudinal imaging data which possesses inherent spatial and tem- poral correlation, we propose a novel procedure to estimate its mean function. Functional moving average is applied to depict the dependence among temporally ordered images and flexible bivariate splines over triangulations are used to handle the irregular domain of im- ages which is common in imaging studies. Both global and local asymptotic properties of the bivariate spline estimator for mean function are established with simultaneous confidence corridors (SCCs) as a theoretical byproduct. Under some mild conditions, the proposed estimator and its accompanying SCCs are shown to be consistent and oracle efficient as if all images were entirely observed without errors. The finite sample performance of the proposed method through Monte Carlo simulation experiments strongly corroborates the asymptotic theory. The proposed method is illustrated by analyzing two sea water potential temperature data sets.