Abstract
It is of great interest to conduct robust functional principal component analysis (FPCA) that can identify the major modes of variation in the stochastic process with the presence of outliers. A new robust FPCA method is proposed in a new regression framework. An M-estimator for the functional principal components is developed based on the Huber’s loss by iteratively fitting the residuals from the Karhunen–Lovève expansion for the stochastic process under the robust regression framework. Our method can naturally accommodate sparse and irregularly-sampled data. When the functional data have outliers, our method is shown to render stable and robust estimates of the functional principal components; when the functional data have no outliers, we show via simulation studies that the performance of our approach is similar to that of the conventional FPCA method. The proposed robust FPCA method is demonstrated by analyzing the Hawaii ocean oxygen data and the kidney glomerular filtration rates for patients after renal transplantation.
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Acknowledgements
The authors would like to thank the Editor, the Associate Editor, and two reviewers for their valuable comments, which are very helpful to improve this work. This work was supported by the discovery grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) to J. Cao and H. Shi.
Funding
Funding was provided by Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada (Grand No. RGPIN-2018-06008)
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Shi, H., Cao, J. Robust Functional Principal Component Analysis Based on a New Regression Framework. JABES 27, 523–543 (2022). https://doi.org/10.1007/s13253-022-00495-1
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DOI: https://doi.org/10.1007/s13253-022-00495-1