Variable selection and estimation for semi-parametric multiple-index models

Tao Wang, Peirong Xu, Lixing ZHU

Research output: Contribution to journalJournal articlepeer-review

11 Citations (Scopus)


In this paper, we propose a novel method to select significant variables and estimate the corresponding coefficients in multiple-index models with a group structure. All existing approaches for single-index models cannot be extended directly to handle this issue with several indices. This method integrates a popularly used shrinkage penalty such as LASSO with the group-wise minimum average variance estimation. It is capable of simultaneous dimension reduction and variable selection, while incorporating the group structure in predictors. Interestingly, the proposed estimator with the LASSO penalty then behaves like an estimator with an adaptive LASSO penalty. The estimator achieves consistency of variable selection without sacrificing the root-n consistency of basis estimation. Simulation studies and a real-data example illustrate the effectiveness and efficiency of the new method.

Original languageEnglish
Pages (from-to)242-275
Number of pages34
Issue number1
Publication statusPublished - 1 Feb 2015

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • Adaptive LASSO
  • Group-wise dimension reduction
  • Minimum average variance estimation
  • Mixed-rates asymptotics
  • Model-free variable selection
  • Sufficient dimension reduction


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