Empirical Likelihood Inference For Partially Observed Functional Data

The problem of completing the partially observed functional data is becoming one of the hot topics for statisticians with the universal application of functional data analysis in various fields.Functional data reconstruction is particularly important because it is the foundational work for classification,regression and inference of partially observed functional data.This thesis focuses on the problem of empirical likelihood inference for the mean function of partially observed functional data combining some relevant reconstruction methods.Under some mild conditions,we prove the asymptotic chi-square property of the log empirical likelihood ratio statistic.Thus by calculating its pseudo-confidence band we propose a shrinkage iterative algorithm of the mean function.Finally,simulation studies and real data analysis are carried out to investigate the validity and the finite-sample performances of our proposed method.