Principal minimax support vector machine for sufficient dimension reduction with contaminated data

Abstract

To make sufficient dimension reduction methods be able to handle contaminated data, a principal minimax support vector machine is suggested to identifying the central subspace. For sparse sufficient dimension reduction, this method of adaptive elastic net type is suggested to make estimation more accurate. The methods are extended to deal with transformed sufficient dimension reduction against contaminated data. The asymptotic unbiasedness and exhaustiveness are proved from the viewpoint of sufficient dimension reduction, and the sparseness and model selection consistency are showed from the viewpoint of variable selection. Simulations and real data analysis are conducted to examine the finite sample performances of the proposed methods.