A Shrinkage Estimation of Central Subspace in Sufficient Dimension Reduction

Abstract

Sliced regression is an effective dimension reduction method by replacing the original high-dimensional predictors with its appropriate low-dimensional projection. It is free from any probabilistic assumption and can exhaustively estimate the central subspace. In this article, we propose to incorporate shrinkage estimation into sliced regression so that variable selection can be achieved simultaneously with dimension reduction. The new method can improve the estimation accuracy and achieve better interpretability for the reduced variables. The efficacy of proposed method is shown through both simulation and real data analysis.