Sparse minimum average variance estimation via the adaptive elastic net when the predictors correlated

Abstract

A new model-free variable selection method was proposed in this article, which is called SMAVE-AdEN. We combined the effective sufficient dimension reduction method MAVE with the variable selection method which is called adaptive Elastic Net (AdEN) to introduce SMAVE-AdEN. The SMAVE-AdEN produces a sparse and accurate estimate when the predictors are highly correlated. The advantage of SMAVE-AdEN is that SMAVE-AdEN extended Adaptive Elastic net (AdEN) to nonlinear and multi-dimensional regression. Also, the SMAVE-AdEN enables MAVE to work with problems were the predictors are highly correlated. In addition, SMAVE-AdEN can exhaustively estimate dimensions, while selecting informative covariates simultaneously. The performance of SMAVE-AdEN is evaluated by both simulation and real data analysis.