A0996
Title: Statistical inference for functional data over high-dimensional domain
Authors: Qirui Hu - Tsinghua University (China)
Lijian Yang - Tsinghua University (China) [presenting]
Abstract: The purpose is to develop 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 an efficient two-step mean estimator, 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 $n^{-1/2}$ is established, supported by consistent estimates of covariance function and quantile of the maximal deviation process. The asymptotic theory extends to two samples without extra difficulty. Extensive Monte Carlo experiments corroborate the theory, and satellite ocean data collected by CMEMS illustrates how the proposed SCR is used.
