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

Abstract

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.

Published at http://dx.doi.org/10.3150/13-BEJ566 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (7)

• Nearly unbiased variable selection under minimax concave penalty
• On the "degrees of freedom" of the lasso
• Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection
• Estimation and testing for partially linear single-index models
• Coordinate-independent sparse sufficient dimension reduction and variable selection
• Sufficient dimension reduction based on an ensemble of minimum average variance estimators
• Mixed-rates asymptotics