References
- Bickel, P. J., and Levina, E. (2008a), “Covariance Regularization by Thresholding,” The Annals of Statistics, 36, 2577–2604.
- ——— (2008b), “Regularized Estimation of Large Covariance Matrices,” The Annals of Statistics, 36, 199–227.
- Bickel, P. J., Ritov, Y., and Tsybakov, A. B. (2009), “Simultaneous Analysis of Lasso and Dantzig Selector,” The Annals of Statistics, 37, 1705–1732.
- Breiman, L., Friedman, J., Stone, C. J., and Olshen, R. A. (1984), Classification and Regression Trees, Boca Raton, FL: CRC Press.
- Bühlmann, P., and Van De Geer, S. (2011), Statistics for High-Dimensional Data: Methods, Theory and Applications, New York: Springer Science & Business Media.
- Cai, T. T., and Zhou, H. H. (2012), “Minimax Estimation of Large Covariance Matrices Under l1-Norm,” Statistica Sinica, 22, 1319–1349.
- Chen, L., and Huang, J. Z. (2012), “Sparse Reduced-Rank Regression for Simultaneous dimension Reduction and Variable Selection,” Journal of the American Statistical Association, 107, 1533–1545.
- Chen, X., Zou, C., and Cook, R. D. (2010), “Coordinate-Independent Sparse Sufficient Dimension Reduction and Variable Selection,” The Annals of Statistics, 38, 3696–3723.
- Cook, R. D. (1994), “On the Interpretation of Regression Plots,” Journal of the American Statistical Association, 89, 177–189.
- ——— (1998), Regression Graphics: Ideas for Studying Regressions Through Graphics, New York: Wiley.
- ——— (2004), “Testing Predictor Contributions in Sufficient Dimension Reduction,” The Annals of Statistics, 32, 1062–1092.
- ——— (2007), “Fisher Lecture: Dimension Reduction in Regression,” Statistical Science, 22, 1–26.
- Cook, R. D., and Forzani, L. (2008), “Principal Fitted Components for Dimension Reduction in Regression,” Statistical Science, 23, 485–501.
- Cook, R. D., Forzani, L., and Rothman, A. J. (2012), “Estimating Sufficient Reductions of the Predictors in Abundant High-dimensional Regressions,” The Annals of Statistics, 40, 353–384.
- Cook, R. D., and Ni, L. (2005), “Sufficient Dimension Reduction via Inverse Regression,” Journal of the American Statistical Association, 100, 410–428.
- Cook, R. D., and Weisberg, S. (1991), “Discussion of ‘Sliced Inverse Regression for Dimension Reduction’,” Journal of the American Statistical Association, 86, 328–332.
- Ding, S., and Cook, R. D. (2014), “Dimension Folding PCA and PFC for Matrix-Valued Predictors,” Statistica Sinica, 24, 463–492.
- ——— (2015a), “Higher-Order Sliced Inverse Regressions,” Wiley Interdisciplinary Reviews: Computational Statistics, 7, 249–257.
- ——— (2015b), “Tensor Sliced Inverse Regression,” Journal of Multivariate Analysis, 133, 216–231.
- Donoho, D. L., Johnstone, I. M., Kerkyacharian, G., and Picard, D. (1995), “Wavelet Shrinkage: Asymptopia?” Journal of the Royal Statistical Society, Series B, 57, 301–369.
- Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties,” Journal of the American statistical Association, 96, 1348–1360.
- Fan, J., and Lv, J. (2008), “Sure Independence Screening for Ultrahigh Dimensional Feature Space,” Journal of the Royal Statistical Society, Series B, 70, 849–911.
- Hall, P., and Li, K.-C. (1993), “On Almost Linearity of Low Dimensional Projections from High Dimensional Data,” The Annals of Statistics, 21, 867–889.
- Hilafu, H., and Yin, X. (2017), “Sufficient Dimension Reduction and Variable Selection for Large-p-small-n Data with Highly Correlated Predictors,” Journal of Computational and Graphical Statistics, 26, 26–34.
- Huang, J., Ma, S., and Zhang, C.-H. (2008), “Adaptive Lasso for Sparse High-Dimensional Regression Models,” Statistica Sinica, 18, 1603–1618.
- Karoui, N. E. (2008), “Operator norm Consistent Estimation of Large-Dimensional Sparse Covariance Matrices,” The Annals of Statistics, 36, 2717–2756.
- Khan, J., Wei, J. S., Ringner, M., Saal, L. H., Ladanyi, M., Westermann, F., Berthold, F., Schwab, M., Antonescu, C. R., Peterson, C., and Meltzer, P. S. (2001), “Classification and Diagnostic Prediction of Cancers using gene Expression Profiling and Artificial Neural Networks,” Nature Medicine, 7, 673–679.
- Lam, C., and Fan, J. (2009), “Sparsistency and Rates of Convergence in Large Covariance Matrix Estimation,” Annals of statistics, 37, 4254–4278.
- Li, B., Kim, M. K., and Altman, N. (2010), “On Dimension Folding of Matrix-or Array-valued Statistical Objects,” The Annals of Statistics, 38, 1094–1121.
- Li, B., and Wang, S. (2007), “On Directional Regression for Dimension Reduction,” Journal of the American Statistical Association, 102, 997–1008.
- Li, K.-C. (1991), “Sliced Inverse Regression for Dimension Reduction,” Journal of the American Statistical Association, 86, 316–327.
- Li, L. (2007), “Sparse Sufficient Dimension Reduction,” Biometrika, 94, 603–613.
- Li, L., and Yin, X. (2008), “Sliced Inverse Regression with Regularizations,” Biometrics, 64, 124–131.
- Li, R., Zhong, W., and Zhu, L. (2012), “Feature Screening via Distance Correlation Learning,” Journal of the American Statistical Association, 107, 1129–1139.
- Lin, Q., Zhao, Z., and Liu, J. S. (2018), “On Consistency and Sparsity for Sliced Inverse Regression in High Dimensions,” The Annals of Statistics, 46, 580–610.
- Ma, Y., and Zhu, L. (2012), “A Semiparametric Approach to Dimension Reduction,” Journal of the American Statistical Association, 107, 168–179.
- Qian, W., Li, W., Sogawa, Y., Fujimaki, R., Yang, X., and Liu, J. (2018), “An Interactive Greedy Approach to Group Sparsity in High Dimension,” preprint arXiv:1707.02963.
- Qian, W., Yang, Y., and Zou, H. (2016), “Tweedie’s Compound Poisson Model with Grouped Elastic Net,” Journal of Computational and Graphical Statistics, 25, 606–625.
- Rothman, A. J. (2012), “Positive Definite Estimators of Large Covariance Matrices,” Biometrika, 99, 733–740.
- Rothman, A. J., Levina, E., and Zhu, J. (2009), “Generalized Thresholding of Large Covariance Matrices,” Journal of the American Statistical Association, 104, 177–186.
- Shao, J., Wang, Y., Deng, X., and Wang, S. (2011), “Sparse Linear Discriminant Analysis by Thresholding for High Dimensional Data,” The Annals of Statistics, 39, 1241–1265.
- Tan, K. M., Wang, Z., Liu, H., and Zhang, T. (2018), “Sparse Generalized Eigenvalue Problem: Optimal Statistical Rates via Truncated Rayleigh Flow,” Journal of the Royal Statistical Society, Series B, accepted.
- Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
- Tseng, P., and Yun, S. (2009), “A Coordinate Gradient Descent Method for Nonsmooth Separable Minimization,” Mathematical Programming, 117, 387–423.
- Wang, H., and Xia, Y. (2008), “Sliced Regression for Dimension Reduction,” Journal of the American Statistical Association, 103, 811–821.
- Wang, T., Zhao, H., Chen, M., and Zhu, L. (2018), “Estimating a Sparse Reduction for General Regression in high Dimensions,” Statistics and Computing, 28, 33–46.
- Wei, F., and Huang, J. (2010), “Consistent Group Selection in High-Dimensional Linear Regression,” Bernoulli, 16, 1369–1384.
- Wu, T. T., and Lange, K. (2010), “The MM Alternative to EM,” Statistical Science, 25, 492–505.
- Wu, Y., and Li, L. (2011), “Asymptotic Properties of Sufficient Dimension Reduction with a Diverging Number of Predictors,” Statistica Sinica, 21, 707–730.
- Xue, L., Ma, S., and Zou, H. (2012), “Positive-Definite l1-Penalized Estimation of Large Covariance Matrices,” Journal of the American Statistical Association, 107, 1480–1491.
- Yin, X., and Hilafu, H. (2015), “Sequential Sufficient Dimension Reduction for Large p, Small n Problems,” Journal of the Royal Statistical Society, Series B, 77, 879–892.
- Yin, X., and Li, B. (2011), “Sufficient Dimension Reduction Based on an Ensemble of Minimum Average Variance Estimators,” The Annals of Statistics, 39, 3392–3416.
- Yu, Z., Dong, Y., and Shao, J. (2016), “On Marginal Sliced Inverse Regression for Ultrahigh Dimensional Model-free Feature Selections,” The Annals of Statistics, 44, 2594–2623.
- Yu, Z., Dong, Y., and Zhu, L.-X. (2016), “Trace Pursuit: A General Framework for Model-free Variable Selection,” Journal of the American Statistical Association, 111, 813–821.
- Yu, Z., Zhu, L., Peng, H., and Zhu, L. (2013), “Dimension Reduction and Predictor Selection in Semiparametric Models,” Biometrika, 100, 641–654.
- Yuan, M., and Lin, Y. (2006), “Model Selection and Estimation in Regression with Grouped Variables,” Journal of the Royal Statistical Society, Series B, 68, 49–67.
- Zhang, C.-H. (2010), “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” The Annals of Statistics, 38, 894–942.
- Zhou, S., van de Geer, S., and Bühlmann, P. (2009), “Adaptive Lasso for high Dimensional Regression and Gaussian Graphical Modeling,” preprint arXiv:0903.2515.
- Zhu, L., Miao, B., and Peng, H. (2006), “On Sliced Inverse Regression with High-Dimensional Covariates,” Journal of the American Statistical Association, 101, 630–643.
- Zhu, L.-P., Li, L., Li, R., and Zhu, L.-X. (2012), “Model-Free Feature Screening for Ultrahigh-Dimensional Data,” Journal of the American Statistical Association, 106, 1464–1475.
- Zou, H. (2006), “The Adaptive Lasso and its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429.
- Zou, H., Hastie, T., and Tibshirani, R. (2006), “Sparse Principal Component Analysis,” Journal of Computational and Graphical Statistics, 15, 265–286.