TY - JOUR
T1 - Asymtotics of Dantzig selector for a general single-index model
AU - Fan, Yan
AU - Gai, Yujie
AU - ZHU, Lixing
N1 - Publisher Copyright:
© 2016, Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed in Gai, Zhu and Lin’s paper in 2013. In this paper, it is further shown that generally the asymptotic equivalence is not true either for a general single-index model with random design of predictors. To achieve this goal, the authors systematically investigate necessary and sufficient conditions for the consistent model selection of the Dantzig selector. An adaptive Dantzig selector is also recommended for the cases where those conditions are not satisfied. Also, different from existing methods for linear models, no distributional assumption on error term is needed with a trade-off that more stringent condition on the predictor vector is assumed. A small scale simulation is conducted to examine the performances of the Dantzig selector and the adaptive Dantzig selector.
AB - As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed in Gai, Zhu and Lin’s paper in 2013. In this paper, it is further shown that generally the asymptotic equivalence is not true either for a general single-index model with random design of predictors. To achieve this goal, the authors systematically investigate necessary and sufficient conditions for the consistent model selection of the Dantzig selector. An adaptive Dantzig selector is also recommended for the cases where those conditions are not satisfied. Also, different from existing methods for linear models, no distributional assumption on error term is needed with a trade-off that more stringent condition on the predictor vector is assumed. A small scale simulation is conducted to examine the performances of the Dantzig selector and the adaptive Dantzig selector.
KW - Adaptive Dantzig Selector
KW - Dantzig selector
KW - general single-index model
KW - model selection consistency
UR - http://www.scopus.com/inward/record.url?scp=84955256105&partnerID=8YFLogxK
U2 - 10.1007/s11424-015-4124-y
DO - 10.1007/s11424-015-4124-y
M3 - Journal article
AN - SCOPUS:84955256105
SN - 1009-6124
VL - 29
SP - 1123
EP - 1144
JO - Journal of Systems Science and Complexity
JF - Journal of Systems Science and Complexity
IS - 4
ER -