Robust functional principal component analysis for non-Gaussian longitudinal data

Abstract

Functional principal component analysis is essential in functional data analysis, but the inference will become unconvincing when non-Gaussian characteristics occur (e.g., heavy tail and skewness). The focus of this manuscript is to develop a robust functional principal component analysis methodology to deal with non-Gaussian longitudinal data, where sparsity and irregularity along with non-negligible measurement errors must be considered. We introduce a Kendall’s τ function to handle the non-Gaussian issues. Moreover, the estimation algorithm is studied and the asymptotic theory is discussed. Our method is validated by a simulation study and it is applied to analyze a real world dataset.