Supervised Principal Component Regression for Functional Responses with High Dimensional Predictors

References

• Bair, E., Hastie, T., Paul, D., and Tibshirani, R. (2006), “Prediction by Supervised Principal Components,” Journal of the American Statistical Association, 101, 119–137. DOI: 10.1198/016214505000000628.
   Web of Science ®Google Scholar
• Barber, R. F., Reimherr, M., and Schill, T. (2017), “The Function-on-Scalar Lasso with Applications to Longitudinal GWAS,” Electron. J. Stat. 11, 1351–1389.
   Web of Science ®Google Scholar
• Bickel, P. J., and Levina, E. (2008), “Regularized Estimation of Large Covariance Matrices,” The Annals of Statistics, 36, 199–227. DOI: 10.1214/009053607000000758.
   Web of Science ®Google Scholar
• Bickel, P. J., Ritov, Y., and Tsybakov, A. B. (2009), “Simultaneous Analysis of Lasso and Dantzig Selector,” The Annals of Statistics, 37, 1705–1732. DOI: 10.1214/08-AOS620.
   Web of Science ®Google Scholar
• Broca, P. (1878), “Anatomie comparée des circonvolutions cérébrales: le grande lobe limbique et la scissure limbique dans la série des mammifères,” Rev D’Anthropol, 1, 385–498.
   Google Scholar
• Cai, T. T., Ren, Z., and Zhou, H. H. (2016), “Estimating Structured High-Dimensional Covariance and Precision Matrices: Optimal Rates and Adaptive Estimation,” Electron. J. Stat. 10, 1–59.
   Web of Science ®Google Scholar
• Chen, Y., Goldsmith, J., and Ogden, T. (2016), “Variable Selection in Function-on-Scalar Regression,” Stat, 5, 88–101. DOI: 10.1002/sta4.106.
   PubMed Web of Science ®Google Scholar
• Desikan, R. S., Ségonne, F., Fischl, B., Quinn, B. T., Dickerson, B. C., Blacker, D., Buckner, R. L., Dale, A. M., Paul Maguire, R., Hyman, B. T., Albert, M. S., and Killiany, R. J. (2006), “An Automated Labeling System for Subdividing the Human Cerebral Cortex on MRI Scans into Gyral based Regions of Interest,” NeuroImage, 31, 968–980. DOI: 10.1016/j.neuroimage.2006.01.021.
   PubMed Web of Science ®Google Scholar
• Ding, X., Yu, D., Zhang, Z., and Kong, D. (2021), “Multivariate Functional Response Low-Rank Regression with an Application to Brain Imaging Data,” Canadian Journal of Statistics, 49, 150–181. DOI: 10.1002/cjs.11604.
   Web of Science ®Google Scholar
• Fan, J., Liu, H., Sun, Q., and Zhang, T. (2018), “I-lamm for Sparse Learning: Simultaneous Control of Algorithmic Complexity and Statistical Error,” Annals of Statistics, 46, 814–841.
   PubMed Web of Science ®Google Scholar
• Faraway, J. J. (1997), “Regression Analysis for a Functional Response,” Technometrics, 39, 254–261. DOI: 10.1080/00401706.1997.10485118.
   Web of Science ®Google Scholar
• Guan, L. (2022), “l1-Norm Constrained Multi-Block Sparse Canonical Correlation Analysis via Proximal Gradient Descent,” arXiv:2201.05289 .
   Google Scholar
• Hariri, A. R., Tessitore, A., Mattay, V. S., Fera, F., and Weinberger, D. R. (2002), “The Amygdala Response to Emotional Stimuli: A Comparison of Faces and Scenes,” NeuroImage, 17, 317–323. DOI: 10.1006/nimg.2002.1179.
   PubMed Web of Science ®Google Scholar
• Hotelling, H. (1957), “The Relations of the Newer Multivariate Statistical Methods to Factor Analysis,” British Journal of Mathematical and Statistical Psychology, 10, 69–79. DOI: 10.1111/j.2044-8317.1957.tb00179.x.
   Web of Science ®Google Scholar
• Kong, D., Xue, K., Yao, F., and Zhang, H. H. (2016), “Partially Functional Linear Regression in High Dimensions,” Biometrika, 103, 147–159. DOI: 10.1093/biomet/asv062.
   Web of Science ®Google Scholar
• Li, G., Yang, D., Nobel, A. B., and Shen, H. (2016), “Supervised Singular Value Decomposition and its Asymptotic Properties,” Journal of Multivariate Analysis, 146, 7–17. DOI: 10.1016/j.jmva.2015.02.016.
   Web of Science ®Google Scholar
• Li, Y., Wang, N., and Carroll, R. J. (2010), “Generalized Functional Linear Models with Semiparametric Single-Index Interactions,” Journal of the American Statistical Association, 105, 621–633. DOI: 10.1198/jasa.2010.tm09313.
   PubMed Web of Science ®Google Scholar
• MacLean, P. D. (1990), The Triune Brain in Evolution: Role in Paleocerebral Functions, New York: Springer.
   Google Scholar
• Mai, Q., Zou, H., and Yuan, M. (2012), “A Direct Approach to Sparse Discriminant Analysis in Ultrahigh Dimensions,” Biometrika, 99, 29–42. DOI: 10.1093/biomet/asr066.
   Web of Science ®Google Scholar
• Negahban, S., and Wainwright, M. J. (2011), “Estimation of (Near) Low-Rank Matrices with Noise and High-Dimensional Scaling,” The Annals of Statistics, 39, 1069–1097. DOI: 10.1214/10-AOS850.
   Web of Science ®Google Scholar
• Preti, M. G., Bolton, T. A., and Van De Ville, D. (2017), “The Dynamic Functional Connectome: State-of-the-Art and Perspectives,” NeuroImage, 160, 41–54. DOI: 10.1016/j.neuroimage.2016.12.061.
   PubMed Web of Science ®Google Scholar
• Tan, K. M., Wang, Z., Liu, H., and Zhang, T. (2018), “Sparse Generalized Eigenvalue Problem: Optimal Statistical Rates via Truncated Rayleigh Flow,” Journal of the Royal Statistical Society, Series B, 80, 1057–1086. DOI: 10.1111/rssb.12291.
   Google Scholar
• Tenenhaus, A., Philippe, C., Guillemot, V., Le Cao, K.-A., Grill, J., and Frouin, V. (2014), “Variable Selection for Generalized Canonical Correlation Analysis,” Biostatistics, 15, 569–583. DOI: 10.1093/biostatistics/kxu001.
   PubMed Web of Science ®Google Scholar
• Witten, D. M., and Tibshirani, R. (2011), “Penalized Classification using Fisher’s Linear Discriminant,” Journal of the Royal Statistical Society, Series B, 73, 753–772. DOI: 10.1111/j.1467-9868.2011.00783.x.
   Google Scholar
• Witten, D. M., Tibshirani, R., and Hastie, T. (2009), “A Penalized Matrix Decomposition, with Applications to Sparse Principal Components and Canonical Correlation Analysis,” Biostatistics, 10, 515–534. DOI: 10.1093/biostatistics/kxp008.
   PubMed Web of Science ®Google Scholar
• Yao, F., Müller, H.-G., and Wang, J.-L. (2005), “Functional Data Analysis for Sparse Longitudinal Data,” Journal of the American Statistical Association, 100, 577–590. DOI: 10.1198/016214504000001745.
   Web of Science ®Google Scholar