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Title: Robust functional principal components analysis with application to accelerometry data Authors:  Chongzhi Di - Fred Hutchinson Cancer Center (United States) [presenting]
Guangxing Wang - US Food and Drug Administration (United States)
Fang Han - University of Washington (United States)
Abstract: Accelerometers are widely used to measure physical activity in biomedical studies objectively. They collect high-resolution functional data, which are often highly skewed and have outliers. Standard functional principal component analysis (FPCA) is based on empirical covariance operators and might not work well in these settings. To address these challenges, we propose a new robust approach for FPCA, based on a functional pairwise spatial sign operator (PASS). Theoretical properties of the proposed method are established. In particular, it is shown that the PASS has the same set of eigenfunctions as the standard covariance operator and that their corresponding eigenvalues are in the same order. Through extensive simulation studies, the proposed robust FPCA is shown to perform well under various types of functional data. We applied the method to an ancillary study of the Women Health Initiative that recorded 7-day accelerometry data on 6500 women.