A0971
Title: Robust functional data analysis for discretely observed data
Authors: Lingxuan Shao - Fudan University (China) [presenting]
Fang Yao - Peking University (China)
Abstract: Robust functional data analysis is considered for discretely observed data with the underlying process having various distributions, such as heavy-tail, skewness, or contaminations. A unified, robust notion of functional mean, covariance, and principal component analysis, are presented, while the existing methods/definitions often differ from each other or concern only fully observed functions (the ideal case). Specifically, the robust functional mean is allowed to be different from its non-robust counterpart and estimated by robust local linear regression, and a new robust functional covariance is defined to share useful properties with the classic version. More importantly, this covariance induces the robust version of Karhunen--Loeve decomposition and corresponding principal components that are useful for dimension reduction. The theoretical results of the robust functional mean, covariance, and eigenfunction estimates, based on pooling discretely observed data (ranging from sparse to dense), are established and coincide with their non-robust counterparts. It is mentioned that the new perturbation bounds for estimated eigenfunctions with indexes allowed to grow with sample size provide a foundation for further modelling based on robust functional principal component analysis.
