×

Envelope methods. (English) Zbl 07909785


MSC:

62-08 Computational methods for problems pertaining to statistics
Full Text: DOI

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.