Regularized MAVE through the elastic net with correlated predictors

Abstract

In this article, we proposed a model-free variable selection method (SMAVE-EN). The concepts of sufficient dimension reduction (SDR) and regularization methods are combined to introduce SMAVE-EN. This method is proposed to produce a shrinkage estimation when the predictors are highly correlated under SDR settings. The advantage of SMAVE-EN is that SMAVE-EN extended Elastic net (EN) to nonlinear and multi-dimensional regression under SDR settings. From another side, the SMAVE-EN enables MAVE to work with problems were the predictors are highly correlated. In addition, SMAVE-EN can exhaustively estimate dimensions, while selecting informative covariates simultaneously under SDR framework. The effectiveness of SMAVE-EN is evaluated by both simulation and real data analysis.