Functional principal component analysis for partially observed elliptical process

The robust principal component estimators for partially observed functional data with heavy-tail behaviors are presented, where sample trajectories are collected over individual-specific subintervals. The method considers partially sampled trajectories as the elliptical process filtered by the missing indicator process and implements robust functional principal component analysis under this framework. The proposed method is computationally efficient and straightforward by estimating the robust correlation function through pairwise covariance computation combined with M-estimation. The asymptotic consistency of the estimators is established under general conditions. The simulation studies demonstrate the superior performance of the method in the approximation of the subspace of data and reconstruction of full trajectories. The proposed method is then applied to hourly monitored air pollutant data containing anomaly trajectories with random missing segments.