References
- Ahn, S. C. , and Horenstein, A. R. (2013), “Eigenvalue Ratio Test for the Number of Factors,” Econometrica , 81, 1203–1227.
- Anderson, T. W. (1951), “Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions,” The Annals of Mathematical Statistics , 22, 327–351. DOI: https://doi.org/10.1214/aoms/1177729580.
- Anderson, T. W. (2004), An Introduction to Multivariate Statistical Analysis (3rd ed.), New York: Wiley.
- Bing, X. , and Wegkamp, M. H. (2019), “Adaptive Estimation of the Rank of the Coefficient Matrix in High-Dimensional Multivariate Response Regression Models,” The Annals of Statistics , 47, 3157–3184. DOI: https://doi.org/10.1214/18-AOS1774.
- Bunea, F. , She, Y. , and Wegkamp, M. H. (2011), “Optimal Selection of Reduced Rank Estimators of High-Dimensional Matrices,” The Annals of Statistics , 39, 1282–1309. DOI: https://doi.org/10.1214/11-AOS876.
- Fan, J. , and Peng, H. (2004), “Nonconcave Penalized Likelihood With a Diverging Number of Parameters,” The Annals of Statistics , 32, 928–961. DOI: https://doi.org/10.1214/009053604000000256.
- Franck, U. , Odeh, S. , Wiedensohler, A. , Wehner, B. , and Herbarth, O. (2011), “The Effect of Particle Size on Cardiovascular Disorders—The Smaller the Worse,” Science of the Total Environment , 409, 4217–4221. DOI: https://doi.org/10.1016/j.scitotenv.2011.05.049.
- Kong, Y. , Li, D. , Fan, Y. , and Lv, J. (2017), “Interaction Pursuit in High-Dimensional Multi-Response Regression via Distance Correlation,” The Annals of Statistics , 45, 897–922. DOI: https://doi.org/10.1214/16-AOS1474.
- 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: https://doi.org/10.1214/10-AOS850.
- Obozinski, G. , Wainwright, M. J. , and Jordan, M. I. (2011), “Support Union Recovery in High-Dimensional Multivariate Regression,” The Annals of Statistics , 39, 1–47. DOI: https://doi.org/10.1214/09-AOS776.
- Polichetti, G. , Cocco, S. , Spinali, A. , Trimarco, V. , and Nunziata, A. (2009), “Effects of Particulate Matter (PM10, PM 2.5 and PM1) on the Cardiovascular System,” Toxicology , 261, 1–8.
- Pun, V. C. , Kazemiparkouhi, F. , Manjourides, J. , and Suh, H. H. (2017), “Long-Term PM 2.5 Exposure and Respiratory, Cancer, and Cardiovascular Mortality in Older US Adults,” American Journal of Epidemiology , 186, 961–969.
- Raskutti, G. , Yuan, M. , and Chen, H. (2019), “Convex Regularization for High-Dimensional Multiresponse Tensor Regression,” The Annals of Statistics , 47, 1554–1584. DOI: https://doi.org/10.1214/18-AOS1725.
- Reinsel, G. C. , and Velu, R. P. (1998), Multivariate Reduced-Rank Regression Theory and Applications , New York: Springer.
- Riediker, M. , Cascio, W. E. , Griggs, T. R. , Herbst, M. C. , Bromberg, P. A. , Neas, L. , Williams, R. W. , and Devlin, R. B. (2004), “Particulate Matter Exposure in Cars Is Associated With Cardiovascular Effects in Healthy Young Men,” American Journal of Respiratory and Critical Care Medicine , 169, 934–940. DOI: https://doi.org/10.1164/rccm.200310-1463OC.
- Xing, Y.-F. , Xu, Y.-H. , Shi, M.-H. , and Lian, Y.-X. (2016), “The Impact of PM2.5 on the Human Respiratory System,” Journal of Thoracic Disease , 8, E69.
- Yuan, M. , Ekici, A. , Lu, Z. , and Monteiro, R. (2007), “Dimension Reduction and Coefficient Estimation in Multivariate Linear Regression,” Journal of the Royal Statistical Society, Series B, 69, 329–346. DOI: https://doi.org/10.1111/j.1467-9868.2007.00591.x.
- Zhang, P. (1993), “Model Selection via Multifold Cross Validation,” The Annals of Statistics , 21, 299–313. DOI: https://doi.org/10.1214/aos/1176349027.
- Zheng, Z. , Bahadori, M. T. , Liu, Y. , and Lv, J. (2019), “Scalable Interpretable Multi-Response Regression via SEED,” Journal of Machine Learning Research , 20, 1–34.
- Zou, H. (2006), “The Adaptive Lasso and Its Oracle Properties,” Journal of the American Statistical Association , 101, 1418–1429. DOI: https://doi.org/10.1198/016214506000000735.