Distributed adaptive lasso penalized generalized linear models for big data

References

• Ai, M., J. Yu, H. Zhang, and H. Wang. 2018. Optimal Subsampling Algorithms for Big Data Generalized Linear Models. arXiv preprint arXiv:1806.06761.
   Google Scholar
• Battey, H., J. Fan, H. Liu, J. Lu, and Z. Zhu. 2015. Distributed Estimation and Inference With Statistical Guarantees. arXiv preprint arXiv:1509.05457.
   Google Scholar
• Boyd, S., N. Parikh, E. Chu, B. Peleato, and J. Eckstein. 2010. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Foundations and Trends® in Machine Learning 3 (1):1–122. doi:10.1561/2200000016.
   Google Scholar
• Cui, Y., X. Chen, and L. Yan. 2017. Adaptive Lasso for Generalized Linear Models with a Diverging Number of Parameters. Communications in Statistics - Theory and Methods 46 (23):11826–42. doi:10.1080/03610926.2017.1285926.
   Web of Science ®Google Scholar
• Efron, B., T. Hastie, I. Johnstone, and R. Tibshirani. 2004. Least Angle Regression. The Annals of Statistics 32 (2):407–99. doi:10.1214/009053604000000067.
   Web of Science ®Google Scholar
• Fan, J., Y. Fan, and E. Barut. 2014. Adaptive Robust Variable Selection. Annals of Statistics 42 (1):324–51. doi:10.1214/13-AOS1191.
   PubMed Web of Science ®Google Scholar
• Fan, J., and R. Li. 2001. Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties. Journal of the American Statistical Association 96 (456):1348–60. doi:10.1198/016214501753382273.
   Web of Science ®Google Scholar
• Friedman, J., T. Hastie, and R. Tibshirani. 2010. Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software 33 (1):1–22. doi:10.18637/jss.v033.i01.
   PubMed Web of Science ®Google Scholar
• Geyer, C. J. 1994. On the Asymptotics of Constrained M-Estimation. The Annals of Statistics 22 (4):1993–2010. doi:10.1214/aos/1176325768.
   Web of Science ®Google Scholar
• Gu, Y., J. Fan, L. Kong, S. Ma, and H. Zou. 2018. ADMM for High-Dimensional Sparse Penalized Quantile Regression. Technometrics 60 (3):319–31. doi:10.1080/00401706.2017.1345703.
   Web of Science ®Google Scholar
• Knight, K., and W. Fu. 2000. Asymptotics for Lasso-Type Estimators. The Annals of Statistics 28 (5):1356–78. doi:10.1214/aos/1015957397.
   Web of Science ®Google Scholar
• Leng, C., and B. Li. 2010. Least Squares Approximation with a Diverging Number of Parameters. Statistics & Probability Letters 80 (3-4):254–61. doi:10.1016/j.spl.2009.10.015.
   Web of Science ®Google Scholar
• Lin, N., and R. Xi. 2011. Aggregated Estimating Equation Estimation. Statistics and Its Interface 4 (1):73–83. doi:10.4310/SII.2011.v4.n1.a8.
   Web of Science ®Google Scholar
• Nelder, J. A., and R. W. Wedderburn. 1972. Generalized Linear Models. Journal of the Royal Statistical Society: Series A (General) 135 (3):370–84. doi:10.2307/2344614.
   Web of Science ®Google Scholar
• Park, M. Y., and T. Hastie. 2007. L1-Regularization Path Algorithm for Generalized Linear Models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 69 (4):659–77.
   Web of Science ®Google Scholar
• Su, X., J. Fan, R. A. Levine, M. E. Nunn, and C.-L. Tsai. 2018. Sparse Estimation of Generalized Linear Models (GLM) via Approximated Information Criteria. Statistica Sinica 28 (3):1561–81.
   Web of Science ®Google Scholar
• Tibshirani, R. 1996. Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58 (1):267–88.
   Web of Science ®Google Scholar
• Wang, H., and C. Leng. 2007. Unified Lasso Estimation by Least Squares Approximation. Journal of the American Statistical Association 102 (479):1039–48. doi:10.1198/016214507000000509.
   Web of Science ®Google Scholar
• Wang, M., L. Song, and X. Wang. 2010. Bridge Estimation for Generalized Linear Models with a Diverging Number of Parameters. Statistics & Probability Letters 80 (21-22):1584–96. doi:10.1016/j.spl.2010.06.012.
   Web of Science ®Google Scholar
• Wang, M., and X. Wang. 2014. Adaptive Lasso Estimators for Ultrahigh Dimensional Generalized Linear Models. Statistics & Probability Letters 89:41–50. doi:10.1016/j.spl.2014.02.015.
   Web of Science ®Google Scholar
• Yu, L., and N. Lin. 2017. ADMM for Penalized Quantile Regression in Big Data. International Statistical Review 85 (3):494–518. doi:10.1111/insr.12221.
   Web of Science ®Google Scholar
• Yu, L., N. Lin, and L. Wang. 2017. A Parallel Algorithm for Large-Scale Nonconvex Penalized Quantile Regression. Journal of Computational and Graphical Statistics 26 (4):935–9. doi:10.1080/10618600.2017.1328366.
   Web of Science ®Google Scholar
• Zhang, C. H. 2010. Nearly Unbiased Variable Selection Under Minimax Concave Penalty. The Annals of Statistics 38 (2):894–942. doi:10.1214/09-AOS729.
   Web of Science ®Google Scholar
• Zou, H. 2006. The Adaptive Lasso and Its Oracle Properties. Journal of the American Statistical Association 101 (476):1418–29. doi:10.1198/016214506000000735.
   Web of Science ®Google Scholar
• Zou, H., and H. H. Zhang. 2009. On the Adaptive Elastic-Net with a Diverging Number of Parameters. Annals of Statistics 37 (4):1733–51. doi:10.1214/08-AOS625.
   PubMed Web of Science ®Google Scholar