报告题目：Statistical Inference for Functional Data over High-dimensional Domain

报告时间：2024-05-28  14:30-16:00

报 告 人：YANG LIJIAN 教授（清华大学）

腾讯会议：381-814-865

Abstract: This work develops inference tools for the mean function of functional data over a high-dimensional domain. Tensor product spline is used to recover individual trajectories, leading to a two-step mean estimator that is oracally efficient, meaning that it is asymptotically indistinguishable from the infeasible estimator using unobservable trajectories. A data-driven SCR with preset asymptotic coverage and uniformly adaptive width of order is established, supported by consistent estimates of covariance function as well as quantile interval of the maximal deviation process. The asymptotic theory extends to two-samples without extra difficulty. Extensive Monte Carlo experiments corroborate the theory, and a satellite ocean data collected by CMEMS illustrates how the proposed SCR is used.