Sliced inverse regression via natural canonical thresholding

References

• Aguilera-Morillo, M. C., R. E. Lillo, and A. Mendez-Civieta. 2021. Adaptive sparse group LASSO in quantile regression. Advances in Data Analysis and Classification 15 (3):547–73. doi:10.1007/s11634-020-00413-8.
   Web of Science ®Google Scholar
• Aragon, Y., and J. Saracco. 1997. Sliced Inverse Regression (SIR): An appraisal of small sample alternatives to slicing. Computational Statistics 12:109–30.
   Web of Science ®Google Scholar
• Bernard-Michel, C., L. Gardes, and S. Girard. 2009. Gaussian regularized sliced inverse regression. Statistics and Computing 19 (1):85–98. doi:10.1007/s11222-008-9073-z.
   Web of Science ®Google Scholar
• Bura, E., and R. D. Cook. 2001. Estimating the structural dimension of regressions via parametric inverse regression. Journal of the Royal Statistical Society Series B: Statistical Methodology 63 (2):393–410. doi:10.1111/1467-9868.00292.
   Web of Science ®Google Scholar
• Bühlmann, P., M. Kalisch, and L. Meier. 2014. High-dimensional statistics with a view toward applications in biology. Annual Review of Statistics and Its Application 1 (1):255–78. doi:10.1146/annurev-statistics-022513-115545.
   Web of Science ®Google Scholar
• Carroll, R. J., and T. Hsing. 1992. An asymptotic theory for sliced inverse regression. The Annals of Statistics 20 (2):1040–61. doi:10.1214/aos/1176348669.
   Web of Science ®Google Scholar
• Chiaromonte, F., and J. Martinelli. 2002. Dimension reduction strategies for analyzing global gene expression data with a response. Mathematical Biosciences 176 (1):123–44. doi:10.1016/s0025-5564(01)00106-7. 11867087.
   PubMed Web of Science ®Google Scholar
• Cook, R. D. 1998. Regression graphics: Ideas for studying regressions through graphics. New York: Wiley.
   Google Scholar
• Cook, R.D. 2007. Fisher lecture: Dimension reduction in regression. Statistical Science 22:1–26.
   Web of Science ®Google Scholar
• Cook, R. D., and B. Li. 2002. Dimension reduction for conditional mean in regression. The Annals of Statistics 30:455–74. doi:10.1214/aos/1021379861
   Google Scholar
• Cook, R. D., and S. Weisberg. 1991. Sliced inverse regression for dimension reduction: Comment. Journal of the American Statistical Association 86 (414):328. doi:10.2307/2290564.
   Web of Science ®Google Scholar
• Duan, N., and K. C. Li. 1991. Slicing regression: A link-free regression method. Journal of the American Statistical Association 19:505–30.
   Google Scholar
• Fan, J., R. Li, C. H. Zhang, and H. Zou, 2020. Statistical foundations of data science. New York: Chapman and Hall.
   Google Scholar
• Fan, J., and I. Silin. 2021. Canonical thresholding for non-sparse high-dimensional linear regression. Annals of Statistics 50 (1):460–86. doi:10.1214/21-aos2116. 36148472.
   Web of Science ®Google Scholar
• Fang, K. T., and L. X. Zhu. 1996. Asymptotics for kernel estimate of sliced inverse regression. The Annals of Statistics 24 (3):1053–68. doi:10.1214/aos/1032526955.
   Web of Science ®Google Scholar
• Lang, W., and H. Zou. 2020. A simple method to improve principal components regression. Journal of Statistics 9 (1):e288. doi:10.1002/sta4.288.
   Google Scholar
• Li, B. 2018. Sufficient dimension reduction: Methods and applications with R. Boca Raton, FL: Chapman and Hall/CRC Press.
   Google Scholar
• Li, K.-C. 1991. Sliced inverse regression for dimension reduction. Journal of the American Statistical Association 86 (414):316. doi:10.2307/2290563.
   Web of Science ®Google Scholar
• Li, L., and H. Li. 2004. Dimension reduction methods for microarrays with application to censored survival data. Bioinformatics 20 (18):3406–12. doi:10.1093/bioinformatics/bth415.
   PubMed Web of Science ®Google Scholar
• Saracco, J. 1997. An asymptotic theory for sliced inverse regression. Communications in Statistics - Theory and Methods 26, 2141–71. doi:10.1080/02331888.2019.1656723.
   Google Scholar
• Schott, J. R. 1994. Determining the dimensionality in sliced inverse regression. Journal of the American Statistical Association 89 (425):141. doi:10.2307/2291210.
   Web of Science ®Google Scholar
• Zhong, W., P. Zeng, P. Ma, J. S. Liu, and Yu. Zhu. 2005. RSIR: Regularized sliced inverse regression for motif discovery. Bioinformatics (Oxford, England) 21 (22):4169–75. doi:10.1093/bioinformatics/bti680. 16166098.
   PubMed Web of Science ®Google Scholar
• Zhu, L-P., and Z. Yu. 2007. On spline approximation of sliced inverse regression. Science in China Series A: Mathematics 50 (9):1289–302. doi:10.1007/s11425-007-0085-5.
   Google Scholar