Consistency and robustness properties of the S-nonnegative garrote estimator

References

• Frank IE, Friedman JH. A statistical view of some chemometrics regression tools. Technometrics. 1993;35(2):109–135. doi: 10.1080/00401706.1993.10485033
   Web of Science ®Google Scholar
• Fu WJ. Penalized regressions: the bridge versus the lasso. J Comput Graph Stat. 1998;7(3):397–416.
   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
• Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Amer Statist Assoc. 2001;96(456):1348–1360. doi: 10.1198/016214501753382273
   Web of Science ®Google Scholar
• Breiman L. Better subset regression using the nonnegative garrote. Technometrics. 1995;37(4):373–384. doi: 10.1080/00401706.1995.10484371
   Web of Science ®Google Scholar
• Wang H, Li G, Jiang G. Robust regression shrinkage and consistent variable selection through the LAD-Lasso. J Bus Econ Stat. 2007;25(3):347–355. doi: 10.1198/073500106000000251
   Web of Science ®Google Scholar
• Arslan O. Weighted LAD-LASSO method for robust parameter estimation and variable selection in regression. Comput Stat Data Anal. 2012;56(6):1952–1965. doi: 10.1016/j.csda.2011.11.022
   Web of Science ®Google Scholar
• Alfons A, Croux C, Gelper S. Sparse least trimmed squares regression for analyzing high-dimensional large data sets. Ann Appl Stat. 2013;7(1):226–248. doi: 10.1214/12-AOAS575
   Web of Science ®Google Scholar
• Öllerer V, Croux C, Alfons A. The influence function of penalized regression estimators. Statistics. 2015;49(4):741–765. doi: 10.1080/02331888.2014.922563
   Web of Science ®Google Scholar
• Wang L, Li R. Weighted Wilcoxon-type smoothly clipped absolute deviation method. Biometr J Int Biometr Soc. 2009;65(2):564–571.
   PubMed Web of Science ®Google Scholar
• Wang X, Jiang Y, Huang M, et al. Robust variable selection with exponential squared loss. J Amer Statist Assoc. 2013;108(502):632–643. doi: 10.1080/01621459.2013.766613
   PubMed Web of Science ®Google Scholar
• Xiong S, Joseph VR. Regression with outlier shrinkage. J Statist Plan Inference. 2013;143:1988–2001. doi: 10.1016/j.jspi.2013.06.007
   Web of Science ®Google Scholar
• Yuan M, Lin Y. On the non-negative garrote estimator. J R Statist Soc Ser B. Statist Methodol. 2007;69(2):143–161. doi: 10.1111/j.1467-9868.2007.00581.x
   Web of Science ®Google Scholar
• Antoniadis A, Gijbels I, Verhasselt A. Variable selection in additive models using P-splines. Technometrics. 2012;54(4):425–438. doi: 10.1080/00401706.2012.726000
   Web of Science ®Google Scholar
• Antoniadis A, Gijbels I, Verhasselt A. Variable selection in varying-coefficient models using P-splines. J Comput Graph Stat. 2012;21(3):638–661. doi: 10.1080/10618600.2012.680826
   Web of Science ®Google Scholar
• Gijbels I, Vrinssen I. Robust nonnegative garrote variable selection in linear regression. Comput Stat Data Anal. 2015;85:1–22. doi: 10.1016/j.csda.2014.11.009
   Web of Science ®Google Scholar
• Yohai VJ. High breakdown-point and high efficiency robust estimates for regression. Ann Stat. 1987;15(2):642–656. doi: 10.1214/aos/1176350366
   Web of Science ®Google Scholar
• Yohai VJ, Zamar RH. High breakdown-point estimates of regression by means of the minimization of an efficient scale. J Amer Statist Assoc. 1988;83(402):406–413. doi: 10.1080/01621459.1988.10478611
   Web of Science ®Google Scholar
• Zou H. The adaptive lasso and its oracle properties. J Amer Statist Assoc. 2006;101(476):1418–1429. doi: 10.1198/016214506000000735
   Web of Science ®Google Scholar
• Wagener J, Dette H. The adaptive lasso in high-dimensional sparse heteroscedastic models. Math Methods Stat. 2013;22(2):137–154. doi: 10.3103/S106653071302004X
   Google Scholar
• Maronna RA, Yohai VJ. Asymptotic behavior of general M-estimates for regression and scale with random carriers. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 1981;58(1):7–20. doi: 10.1007/BF00536192
   Web of Science ®Google Scholar
• Chatterjee A, Lahiri SN. Strong consistency of Lasso estimators. Sankhya A: Indian J Stat. 2011;73(1):55–78. doi: 10.1007/s13171-011-0006-0
   Google Scholar
• Ip W, Yang Y, Kwan P, et al. Strong convergence rate of the least median absolute estimator in linear regression models. Statist Pap. 2003;44:183–201. doi: 10.1007/s00362-003-0145-z
   Web of Science ®Google Scholar
• Donoho D, Huber PJ. The notion of breakdown point. In: A Festschrift for Erich L. Lehmann. Belmont, CA: Wadsworth; 1983. p. 157–184. (Wadsworth Statist./Probab. Ser.).
   Google Scholar
• Maronna RA, Martin RD, Yohai VJ. Robust statistics. Chichester: Wiley; 2006. (Wiley Series in Probability and Statistics. Theory and Methods).
   Google Scholar
• Yohai VJ, Zamar RH. Optimal locally robut M-estimates of regression. J Statist Plan Inference. 1997;64:309–323. doi: 10.1016/S0378-3758(97)00040-2
   Web of Science ®Google Scholar
• Kuhn HW, Tucker AW. Nonlinear programming. Proceedings of 2nd Berkeley Symposium. Berkeley: University of California Press;1951. p. 481–492.
   Google Scholar
• Boyd S, Vandenberghe L. Convex optimization. Cambridge: Cambridge University Press; 2004.
   Google Scholar