Covariance estimation for derivatives of functional data using an additive penalty in P-splines
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914344268201984 |
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| author | Zhu, Yueyun Golovkine, Steven Bargary, Norma Simpkin, Andrew J. |
| author_facet | Zhu, Yueyun Golovkine, Steven Bargary, Norma Simpkin, Andrew J. |
| contents | 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. We propose a method which incorporates the fast covariance estimation (FACE) algorithm with an additive penalty in P-splines. 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). Following this, we provide an algorithm for estimating the eigenfunctions and their corresponding scores in derivative-based FPCA. For comparison, we evaluate our algorithm against an existing function \texttt{FPCAder()} in simulation. In addition, we extend the algorithm to multivariate cases, referred to as derivative 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20029 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Covariance estimation for derivatives of functional data using an additive penalty in P-splines Zhu, Yueyun Golovkine, Steven Bargary, Norma Simpkin, Andrew J. Methodology 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. We propose a method which incorporates the fast covariance estimation (FACE) algorithm with an additive penalty in P-splines. 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). Following this, we provide an algorithm for estimating the eigenfunctions and their corresponding scores in derivative-based FPCA. For comparison, we evaluate our algorithm against an existing function \texttt{FPCAder()} in simulation. In addition, we extend the algorithm to multivariate cases, referred to as derivative 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. |
| title | Covariance estimation for derivatives of functional data using an additive penalty in P-splines |
| topic | Methodology |
| url | https://arxiv.org/abs/2602.20029 |