Feature filter for estimating central mean subspace and its sparse solution

Abstract

Sufficient dimension reduction, replacing the original predictors with a few linear combinations while keeping all the regression information, has been widely studied. A key goal is to find the central mean subspace, the intersection of all subspaces that provide such a reduction. To this end, a new sufficient dimension reduction method is proposed, with two estimation procedures, through a novel approach of feature filter, applicable to both univariate and multivariate responses. Asymptotic results are established. Estimation methods to determine the structural dimension, to obtain sparse estimator and to deal with large p small n data are provided. The efficacy of the method is demonstrated by simulations and a real data example.