Abstract
Modern neuroimaging research calls for statistical methods that can model dynamic relationships between a functional response and a set of covariates. Current methods, however, remain disparate and limited in their ability to robustly accommodate real-world data and integrate smoothness penalties. In this work, we propose an M-estimation framework for the varying-coefficient model with a functional response that encompasses both mean and quantile regression. To accommodate smoothness regularization and circumvent the stringent conditions on Fourier coefficients or the covariance operator’s eigenvalues imposed by traditional fixed-basis representations, we assume that the functional coefficient resides in a reproducing kernel Hilbert space. We show that our proposed estimator is minimax rate optimal and establish convergence properties of our modified alternating direction method of multipliers algorithm. We further propose combining a weighted M-estimator and a copula model to quantify within-subject spatial dependence to improve estimation accuracy. Simulation studies and a real-world analysis demonstrate the robustness of our proposed methods to outliers.
Funding Statement
Dr. Jiang and Dr. Kong were supported by the Canada CIFAR AI Chairs program, the Alberta Machine Intelligence Institute, and Natural Sciences and Engineering Council of Canada, and the Canadian Statistical Sciences Institute. Dr. Kong was also supported by the Canada Research Chair program from NSERC. Dr. Zhang was supported by the National Natural Science Foundation of China, No. 12271014.
Acknowledgements
Data used in the preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.
Citation
Yafei Wang. Bei Jiang. Linglong Kong. Zhongzhan Zhang. "M-estimation for varying coefficient models with a functional response in a reproducing kernel Hilbert space." Bernoulli 30 (3) 1998 - 2025, August 2024. https://doi.org/10.3150/23-BEJ1661
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