Asymtotics of Dantzig selector for a general single-index model

Yan Fan*, Yujie Gai, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1123-1144
Number of pages22
JournalJournal of Systems Science and Complexity
Volume29
Issue number4
DOIs
Publication statusPublished - 1 Aug 2016

Scopus Subject Areas

  • Computer Science (miscellaneous)
  • Information Systems

User-Defined Keywords

  • Adaptive Dantzig Selector
  • Dantzig selector
  • general single-index model
  • model selection consistency

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