A1768
Title: Covariance estimation for derivatives of functional data using an additive penalty in P-splines
Authors: Steven Golovkine - Université Laval (Canada) [presenting]
Yueyun Zhu - University of Galway (Ireland)
Andrew Simpkin - University of Galway (Ireland)
Norma Bargary - University of Limerick (Ireland)
Abstract: P-splines provide a flexible and computationally efficient smoothing framework and are commonly used for derivative estimation in functional data. Including an additive penalty term in P-splines has been shown to improve estimates of derivatives. A method that incorporates the fast covariance estimation (FACE) algorithm with an additive penalty in P-splines is proposed. The proposed method is used to estimate derivatives of covariance for functional data, which play an important role in derivative-based functional principal component analysis (FPCA). An algorithm for estimating the eigenfunctions and their corresponding scores in derivative-based FPCA is provided. The algorithm is evaluated against existing functions in simulation. The algorithm is extended to multivariate cases, referred to as derivative-based multivariate functional principal component analysis (DMFPCA). DMFPCA is applied to joint angles in human movement data, where the derivative-based scores demonstrate strong performance in distinguishing locomotion tasks.
