[1] |
Cook, R. D. (1998). Regression graphics. New York, NY: Wiley. · Zbl 0903.62001 |
[2] |
Cook, R. D. (2007). Fisher lecture: Dimension reduction in regression. Statistical Science, 22(1), 1-26. Retrieved from https://projecteuclid.org/euclid.ss/1185975631. https://doi.org/10.1214/088342306000000682 · Zbl 1246.62148 · doi:10.1214/088342306000000682 |
[3] |
Cook, R. D. (2018). An introduction to envelopes. Hoboken, NJ: Wiley. · Zbl 1407.62014 |
[4] |
Cook, R. D., & Forzani, L. (2017). Big data and partial least squares prediction. The Canadian Journal of Statistics/La Revue Canadienne de Statistique, to appear, 46, 62-78. https://doi.org/10.1002/cjs.11316 · Zbl 1466.62367 · doi:10.1002/cjs.11316 |
[5] |
Cook, R. D., & Forzani, L. (2019). Partial least squares prediction in high‐dimensional regression. The Annals of Statistics, 47(2), 884-908. · Zbl 1416.62389 |
[6] |
Cook, R. D., Forzani, L., & Su, Z. (2016). A note on fast envelope estimation. Journal of Multivariate Analysis, 150, 42-54. https://doi.org/10.1016/j.jmva.2016.05.006 · Zbl 1345.62082 · doi:10.1016/j.jmva.2016.05.006 |
[7] |
Cook, R. D., Forzani, L., & Zhang, X. (2015). Envelopes and reduced‐rank regression. Biometrika, 102(2), 439-456. https://doi.org/10.1093/biomet/asv001 · Zbl 1452.62484 · doi:10.1093/biomet/asv001 |
[8] |
Cook, R. D., Helland, I. S., & Su, Z. (2013). Envelopes and partial least squares regression. Journal of the Royal Statistical Society B, 75(5), 851-877. https://doi.org/10.1111/rssb.12018 · Zbl 1411.62137 · doi:10.1111/rssb.12018 |
[9] |
Cook, R. D., Li, B., & Chiaromonte, F. (2007). Dimension reduction in regression without matrix inversion. Biometrika, 94(3), 569-584. https://doi.org/10.1093/biomet/92.4.937 · Zbl 1151.62301 · doi:10.1093/biomet/92.4.937 |
[10] |
Cook, R. D., Li, B., & Chiaromonte, F. (2010). Envelope models for parsimonious and efficient multivariate linear regression. Statistica Sinica, 20(3), 927-960. · Zbl 1259.62059 |
[11] |
Cook, R. D., & Su, Z. (2013). Scaled envelopes: Scale‐invariant and efficient estimation in multivariate linear regression. Biometrika, 100(4), 939-954. https://doi.org/10.1093/biomet/ast026 · Zbl 1452.62492 · doi:10.1093/biomet/ast026 |
[12] |
Cook, R. D., & Su, Z. (2016). Scaled predictor envelopes and partial least‐squares regression. Technometrics, 58(2), 155-165. https://doi.org/10.1080/00401706.2015.1017611 · doi:10.1080/00401706.2015.1017611 |
[13] |
Cook, R. D., & Zhang, X. (2015a). Foundations for envelope models and methods. Journal of the American Statistical Association, 110(510), 599-611. https://doi.org/10.1080/01621459.2014.983235 · Zbl 1390.62131 · doi:10.1080/01621459.2014.983235 |
[14] |
Cook, R. D., & Zhang, X. (2015b). Simultaneous envelopes for multivariate linear regression. Technometrics, 57(1), 11-25. https://doi.org/10.1080/00401706.2013.872700 · doi:10.1080/00401706.2013.872700 |
[15] |
Cook, R. D., & Zhang, X. (2016). Algorithms for envelope estimation. Journal of Computational and Graphical Statistics, 25(1), 284-300. https://doi.org/10.1080/10618600.2015.1029577 · doi:10.1080/10618600.2015.1029577 |
[16] |
Cook, R. D., & Zhang, X. (2018). Fast envelope algorithms. Statistica Sinica, 28, 1179-1197. https://doi.org/10.5705/ss.202016.0037 · Zbl 1394.62067 · doi:10.5705/ss.202016.0037 |
[17] |
Cox, D. R., & Mayo, D. G. (2010). II Objectivity and conditionality in frequentist inference. In D. G.Mayo (ed.) & A.Spanos (ed.) (Eds.), Error and inference: Recent exchanges on experimental reasoning, reliability, and the objectivity and rationality of science (pp. 276-304). Cambridge, England: Cambridge University Press. · Zbl 1257.00006 |
[18] |
deJong, S. (1993). SIMPLS: An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18(3), 251-263. https://doi.org/10.1016/0169-7439(93)85002-X · doi:10.1016/0169-7439(93)85002-X |
[19] |
Ding, S., & Cook, R. D. (2018). Matrix‐variate regressions and envelope models. Journal of the Royal Statistical Society B, 80, 387-408. https://doi.org/10.1111/rssb.12247 · Zbl 06849260 · doi:10.1111/rssb.12247 |
[20] |
Ding, S., Su, Z., Zhu, G., & Wang, L. (2019). Envelope quantile regression. Statistica Sinica. Retrieved from http://www3.stat.sinica.edu.tw/ss_newpaper/SS-2018-0060_na.pdf |
[21] |
Eck, D. J., & Cook, R. D. (2017). Weighted envelope estimation to handle variability in model selection. Biometrica, 104(3), 743-749. https://doi.org/10.1093/biomet/asx035 · Zbl 07072240 · doi:10.1093/biomet/asx035 |
[22] |
Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 222(594-604), 309-368. Retrieved from http://rsta.royalsocietypublishing.org/content/222/594-604/309. https://doi.org/10.1098/rsta.1922.0009 · JFM 48.1280.02 · doi:10.1098/rsta.1922.0009 |
[23] |
Khare, K., Pal, S., & Su, Z. (2016). A Bayesian approach for envelope models. Annals of Statistics, 45(1), 196-222. Retrieved from http://projecteuclid.org/euclid.aos/1487667621. https://doi.org/10.1214/16-AOS1449 · Zbl 1367.62174 · doi:10.1214/16-AOS1449 |
[24] |
Li, B. (2018). Sufficient dimension reduction: Methods and applications with r. New York, NY: Chapman and Hall/CRC Press. · Zbl 1408.62011 |
[25] |
Li, G., Yang, D., Nobel, A. B., & Shen, H. (2015). Supervised singular value decomposition and its asymptotic properties. Journal of Multivariate Analysis, 146, 7-17. Retrieved from. https://doi.org/10.1016/j.jmva.2015.02.016 · Zbl 1336.62129 · doi:10.1016/j.jmva.2015.02.016 |
[26] |
Li, L., & Zhang, X. (2017). Parsimonious tensor response regression. Journal of the American Statistical Association, 112(519), 1131-1146. https://doi.org/10.1080/01621459.2016.1193022 · doi:10.1080/01621459.2016.1193022 |
[27] |
Park, Y., Su, Z., & Zhu, H. (2017). Groupwise envelope models for imaging genetic analysis. Biometrics, 73(4), 1243-1253. https://doi.org/10.1111/biom.12689 · Zbl 1405.62197 · doi:10.1111/biom.12689 |
[28] |
Reinsel, G. C., & Velu, R. P. (1998). Multivariate reduced‐rank regression: Theory and applications. New York, NY: Springer. · Zbl 0909.62066 |
[29] |
Rekabdarkolaee, H. M., Wang, Q., Naji, Z., & Fluentes, M. (2017). New parsimonious multivariate spatial model: Spatial envelope. Statistica Sinica Retrieved from http://www3.stat.sinica.edu.tw/ss_newpaper/SS-2017-0455_na.pdf |
[30] |
Rimal, R., Almoy, T., & Saebo, S. (2019, March). Comparison of multi‐response prediction methods. (arXiv:1903.08426v1) |
[31] |
Su, Z., & Cook, R. D. (2011). Partial envelopes for efficient estimation in multivariate linear regression. Biometrika, 98(1), 133-146. https://doi.org/10.1093/biomet/asq063 · Zbl 1214.62062 · doi:10.1093/biomet/asq063 |
[32] |
Su, Z., & Cook, R. D. (2012). Inner envelopes: Efficient estimation in multivariate linear regression. Biometrika, 99(3), 687-702. https://doi.org/10.1093/biomet/ass024 · Zbl 1437.62619 · doi:10.1093/biomet/ass024 |
[33] |
Su, Z., & Cook, R. D. (2013). Estimation of multivariate means with heteroscedastic errors using envelope models. Statistica Sinica, 23(1), 213-230. https://doi.org/10.5705/ss.2010.240 · Zbl 1259.62045 · doi:10.5705/ss.2010.240 |
[34] |
Su, Z., Zhu, G., Chen, X., & Yang, Y. (2016). Sparse envelope model: Estimation and response variable selection in multivariate linear regression. Biometrika, 103(3), 579-593. https://doi.org/10.1093/biomet/asw036 · Zbl 1495.62056 · doi:10.1093/biomet/asw036 |
[35] |
Zhang, X., & Li, L. (2017). Tensor envelope partial least‐squares regression. Technometrics, 59(4), 426-436. https://doi.org/10.1080/00401706.2016.1272495 · doi:10.1080/00401706.2016.1272495 |
[36] |
Zhang, X., & Mai, Q. (2018). Model‐free envelope dimension selection. Electronic Journal of Statistics, 12(2), 2193-2216. Retrieved from https://projecteuclid.org/euclid.ejs/1531814505 (https://arxiv.org/abs/1709.03945). https://doi.org/10.1214/18-EJS1449 · Zbl 1410.62086 · doi:10.1214/18-EJS1449 |
[37] |
Zhang, X., & Mai, Q. (2019). Efficient integration of sufficient dimension reduction and prediction in discriminant analysis. Technometrics, 61(2), 259-272. |
[38] |
Zhu, G., & Su, Z. (2019). Envelope‐based sparse partial least squares. Annals of Statistics, 47, To appear. https://doi.org/10.1080/00401706.2016.1272495 · doi:10.1080/00401706.2016.1272495 |