Robust FPCA via Functional Pairwise Spatial Sign Robust Functional Principal Component Analysis via a Functional Pairwise Spatial Sign Operator

• Activity Number: 89 - Nonparametric Methods for Modern Data
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Guangxing Wang* and Chongzhi Di and Fang Han and Sisheng Liu
• Companies: Fred Hutchinson Cancer Research Center and Fred Hutchinson Cancer Research Center and University of Washington and Kuaishou technology
• Keywords: Functional elliptical distribution; Functional pairwise spatial sign; Robust FPCA; Weakly FCS

Abstract

In this talk, we present a new robust functional principal component analysis approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA. This includes robust estimation procedures for eigenfunctions and eigenvalues. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. The robustness of the PASS FPCA will be demonstrated via extensive simulation studies, especially its advantages in scenarios with asymmetric distributions. We will also look at an application to the accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, which is a large-scale epidemiological study that investigates the relationship between objectively measured physical activity and cardiovascular health among older women.