Department of Mathematics
Variable selection and estimation for semi-parametric multiple-index models
© 2015 ISI/BS. 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.
Adaptive LASSO, Group-wise dimension reduction, Minimum average variance estimation, Mixed-rates asymptotics, Model-free variable selection, Sufficient dimension reduction
Source Publication Title
Bernoulli Society for Mathematical Statistics and Probability
Link to Publisher's Edition
Wang, T., Xu, P., & Zhu, L. (2015). Variable selection and estimation for semi-parametric multiple-index models. Bernoulli, 21 (1), 242-275. https://doi.org/10.3150/13-BEJ566