References
- Bai, Z. D. 1999. Methodologies in spectral analysis of large dimensional random matrices, a review. Statistica Sinica 9:611–77.
- Bai, J., and K. Li. 2012. Statistical analysis of factor models of high dimension. The Annals of Statistics 40 (1):436–65. doi: 10.1214/11-AOS966.
- Bai, Z. D., and J. W. Silverstein. 2004. CLT for linear spectral statistics of large-dimensional sample covariance matrices. The Annals of Probability 32 (1A):553–605. doi: 10.1214/aop/1078415845.
- Carroll, R. J., D. Ruppert, L. A. Stefanski, and C. Crainiceanu. 2006. Measurement error in nonlinear models: A modern perspective, 2nd Ed. Boca Raton, FL: Chapman and Hall.
- Chow, T. L., and J. L. Teugels. 1978. The sum and the maximum of i.i.d. random variables. In Proceedings of the Second Prague Symposium on Asymptotic Statistics, North Holland, N.Y.
- Dalayan, A., M. Hebiri, and J. Lederer. 2014. On the prediction performance of the lasso. Arxiv:1402.1700v1.
- Fan, J., and R. Song. 2010. Sure independence screening in generalized linear models with np-dimensionality. The Annals of Statistics 38 (6):3567–604. doi: 10.1214/10-AOS798.
- Fan, J., and C. Y. Tang. 2010. Tuning parameter selection in high dimensional penalized likelihood. Journal of the Royal Statistical Society Series B 75 (3):531–52. doi:10.1111/rssb.12001.
- Fan, J., and J. Lv. 2010. A selective overview of variable selection in high dimensional feature space. Statistica Sinica 20 (1):101–48.
- Fan, J., and J. Lv. 2008. Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 70 (5):849–911. doi: 10.1111/j.1467-9868.2008.00674.x.
- Fan, J., R. Samworth, and Y. Wu. 2009. Ultrahigh dimensional feature selection: Beyond the linear model. J. Machine Learning Research 10:1829–53.
- Geman, S. 1980. A limit theorem for the norm of random matrices. The Annals of Probability 8 (2):252–61. doi: 10.1214/aop/1176994775.
- Li, R., W. Zhong, and L. Zhu. 2012. Feature screening via distance correlation learning. Journal of the American Statistical Association 107 (499):1129–39. doi: 10.1080/01621459.2012.695654.
- Meinshausen, N., and P. Bühlmann. 2006. High-dimensional graphs and variable selection with the LASSO. The Annals of Statistics 34 (3):1436–62. doi: 10.1214/009053606000000281.
- Ng, C. T., S. Oh, and Y. Lee. 2016. Going beyond oracle property: Selection consistency and uniqueness of local solution of the generalized linear model. Statistical Methodology 32:147–60. doi: 10.1016/j.stamet.2016.05.006.
- Ng, C. T., C. Y. Yau, and N. H. Chan. 2015. Likelihood inferences for high-dimensional factor analysis of time series with applications in finance. Journal of Computational and Graphical Statistics 24 (3):866–84. doi: 10.1080/10618600.2014.937951.
- Pastur, L., and V. Marcenko. 1967. Distribution of eigenvalues for some sets of random matrices. Mathematics of the USSR-Sbornik 1 (4):457–83. doi: 10.1070/SM1967v001n04ABEH001994.
- Radchenko, P. and G. M. James. 2011. Improved variable selection with Forward-Lasso Adaptive Shrinkage. The Annals of Applied Statistics 5 (1):427–48. doi:10.1214/10-AOAS375.
- Rocke, D. M., and B. Durbin. 2001. A model for measurement error for gene expression arrays. Journal of Computational Biology: A Journal of Computational Molecular Cell Biology 8 (6):557–69. doi: 10.1089/106652701753307485.
- Rothman, K. J., S. Greenland, and T. L. Lash. 2008. Modern epidemiology, 3rd ed. Philadelphia, PA: Lippincott Williams & Wilkins..
- Scheetz, T. E., K.-Y. Kim, R. E. Swiderski, A. R. Philp, T. A. Braun, K. L. Knudtson, A. M. Dorrance, G. F. DiBona, J. Huang, T. L. Casavant, et al. 2006. Regulation of gene expression in the mammalian eye and its relevance to eye disease. Proceedings of the National Academy of Sciences of the United States of America 103 (39):14429–34. doi: 10.1073/pnas.0602562103.
- Silverstein, J. W. 1985. The smallest eigenvalue of a large dimensional Wishart matrix. The Annals of Probability 13 (4):1364–68. doi: 10.1214/aop/1176992819.
- Stamey, T. A., J. N. Kabalin, J. E. McNeal, I. M. Johnstone, F. Freiha, E. A. Redwine, and N. Yang. 1989. Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate: II. radical prostatectomy treated patients. The Journal of Urology 141 (5):1076–83. doi: 10.1016/S0022-5347(17)41175-X.
- Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58 (1):267–88. doi: 10.1111/j.2517-6161.1996.tb02080.x.
- Tibshirani, R. J. 2013. The lasso problem and uniqueness. Electronic Journal of Statistics 7 (0):1456–90. doi: 10.1214/13-EJS815.
- Wang, H., B. Li, and C. Leng. 2009. Shrinkage tuning parameter selection with a diverging number of parameters. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71 (3):671–83. doi: 10.1111/j.1467-9868.2008.00693.x.
- Wang, H., R. Li, and C. L. Tsai. 2007. Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika 94 (3):553–68. doi: 10.1093/biomet/asm053.
- Yuan, M., and Y. Lin. 2007. Model selection and estimation in the Gaussian graphical model. Biometrika 94 (1):19–35. doi: 10.1093/biomet/asm018.
- Zhao, P., and B. Yu. 2006. On model selection consistency of Lasso. Journal of Machine Learning Research 7:2541–63.
- Zhang, C., and J. Huang. 2008. The sparsity and bias of the LASSO selection in high-dimensional linear regression. The Annals of Statistics 36 (4):1567–94. doi: 10.1214/07-AOS520.
- Zhang, C., and T. Zhang. 2012. A general theory of concave regularization for high-dimensional sparse estimation problems. Statistical Science 27 (4):576–93. doi: 10.1214/12-STS399.