Pruning a sufficient dimension reduction with a p-value guided hard-thresholding

References

• Li KC. Slice inverse regression for dimension reduction. J Am Statist Assoc. 1991;86:316–327. doi: 10.1080/01621459.1991.10475035
   Web of Science ®Google Scholar
• Cook RD, Weisberg S. Discussion of Li (1991). J Am Statist Assoc. 1991;86:328–332.
   Web of Science ®Google Scholar
• Li B, Wang S. On directional regression for dimension reduction. J Am Statist Assoc. 2007;102(479):997–1008. doi: 10.1198/016214507000000536
   Web of Science ®Google Scholar
• Cook RD. Fisher lecture - dimension reduction in regression (with discussion). Statist Sci. 2007;22:1–26. doi: 10.1214/088342306000000682
   Web of Science ®Google Scholar
• Donoho DL, Johnstone IM. Adapting to unknown smoothness via wavelet shrinkage. J Am Statist Assoc. 1995;90:1200–1224. doi: 10.1080/01621459.1995.10476626
   Web of Science ®Google Scholar
• Fryzlewicz P. Bivariate hard thresholding in wavelet function estimation. Statist Sin. 2007;17:1457–1481.
   Web of Science ®Google Scholar
• McCabe GP. Principal variables. Technometrics. 1984;26:137–144. doi: 10.1080/00401706.1984.10487939
   Web of Science ®Google Scholar
• Cadima J, Jolliffe IT. Loading and correlations in the interpretation of principal components. J Appl Stat. 1995;22:203–214. doi: 10.1080/757584614
   Web of Science ®Google Scholar
• Jolliffe I. Principal component analysis. New York: Springer; 1995.
   Google Scholar
• Jolliffe IT, Trendafilov NT, Uddin M. A modified principal component technique based on the lasso. J Comput Graph Stat. 2003;12(3):531–547. doi: 10.1198/1061860032148
   Web of Science ®Google Scholar
• Zou H, Hastie T, Tibshirani R. Sparse principal component analysis. J Comput Graph Stat. 2006;15:265–286. doi: 10.1198/106186006X113430
   Web of Science ®Google Scholar
• Tibshirani R. Regression shrinkage and selection via the lasso. J R Statist Soc. Ser B (Methodol). 1996;58(1):267–288.
   Google Scholar
• Li L. Sparse sufficient dimension reduction. Biometrika. 2007;94:603–613. doi: 10.1093/biomet/asm044
   Web of Science ®Google Scholar
• Chun H, Keles¸ S. Sparse partial least squares regression for simultaneous dimension reduction and variable selection. J R Stat Soc: Ser B (Statist Methodol). 2010;72(1):3–25. doi: 10.1111/j.1467-9868.2009.00723.x
   Google Scholar
• Cook RD. Testing predictor contributions in sufficient dimension reduction. Ann Stat. 2004;32(3): 1062–1092. doi: 10.1214/009053604000000292
   Web of Science ®Google Scholar
• Cook RD, Forzani L. Principal fitted components for dimension reduction in regression. Statist Sci. 2008;23(4):485–501. doi: 10.1214/08-STS275
   Web of Science ®Google Scholar
• Fan J, Lv J. Sure independence screening for ultrahigh dimensional feature space. J R Statist Soc: Ser B (Statist Methodol). 2008;70:849–911. doi: 10.1111/j.1467-9868.2008.00674.x
   PubMed Web of Science ®Google Scholar
• Adragni KP. Independent screening in high-dimensional exponential family predictors' space. J Appl Stat. 2015;42(2):347–359. doi: 10.1080/02664763.2014.949640
   Web of Science ®Google Scholar
• Adragni KP, Cook RD. Sufficient dimension reduction and prediction in regression. Philos Trans R Soc, Ser A. 2009;367(1906):4385–4405. doi: 10.1098/rsta.2009.0110
   Web of Science ®Google Scholar
• Hastie T, Tibshirani R, Friedman J. The elements of statistical learning - data mining, inference, and prediction. New York: Springer; 2001.
   Google Scholar
• Kong E, Xia Y. Variable selection for the single-index model. Biometrika. 2007;94(1):217–229. doi: 10.1093/biomet/asm008
   Web of Science ®Google Scholar
• Efron B, Hastie T, Johnstone I, Tibshirani R. Least angle regression. Ann Stat. 2004;32(2):407–499. doi: 10.1214/009053604000000067
   Web of Science ®Google Scholar
• R Development Core Team. A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; 2013. Available from: http://www.R-project.org/.
   Google Scholar
• Enz R. Prices and Earnings Around the Globe. Zurich: Union Bank of Switzerland; 1991.
   Google Scholar
• Friedman J, Hastie T, Tibshirani R. Regularization paths for generalized linear models via coordinate descent. J Statist Softw. 2010;33(1):1–22.
   PubMed Web of Science ®Google Scholar
• Adragni KP, Raim A. An R software package for likelihood-based sufficient dimension reduction. J Statist Softw. 2014;61(3). Available from: http://www.jstatsoft.org/v61/i03.
   Web of Science ®Google Scholar
• Cook RD. Regression graphics. New York: Wiley; 1998.
   Google Scholar
• Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Statist Soc, Ser B. 1995;57(1):289–300.
   Google Scholar
• Zou H, Hastie T. Regularization and variable selection via the Elastic Net. J R Statist Soc: Ser B (Statist Methodol). 2005;67(Part 2):301–320. doi: 10.1111/j.1467-9868.2005.00503.x
   Google Scholar
• Anderson TW. An introduction to multivariate statistical analysis. 3rd ed. Hoboken (NJ): Wiley; 2003.
   Google Scholar
• Bair E, Hastie T, Paul D, Tibshirani R. Prediction by supervised principal components. J Am Statist Assoc. 2006;101(473):119–137. doi: 10.1198/016214505000000628
   Web of Science ®Google Scholar
• Chen X, Zou C, Cook RD. Coordinate-independent sparse sufficient dimension reduction and variable selection. Ann Stat. 2010;38(6):3696–3723. doi: 10.1214/10-AOS826
   Web of Science ®Google Scholar