Penalized principal logistic regression for sparse sufficient dimension reduction

Sufficient dimension reduction (SDR) is a successive tool for reducing the dimensionality of predictors by finding the central subspace, a minimal subspace of predictors that preserves all the regression information. When predictor dimension is large, it is often assumed that only a small number of predictors is informative. In this regard, sparse SDR is desired to achieve variable selection and dimension reduction simultaneously. We propose a principal logistic regression (PLR) as a new SDR tool and extend it to a penalized version for sparse SDR. Asymptotic analysis shows that the penalized PLR enjoys the oracle property. Numerical investigation supports the advantageous performance of the proposed methods