Applications of sufficient dimension reduction algorithms on non-elliptical data

Sufficient dimension reduction (SDR) is a class of supervised dimension reduction techniques which generally perform much better than unsupervised dimension reduction techniques like Principal Component Analysis (PCA). In this paper we present classic methodology in the SDR framework that is based on inverse moments and we discuss the theoretical assumptions. At the end we demonstrate the advantage of a recently introduced method known as Principal Support Vector Machine (PSVM) in the presence of predictors which violate the theoretical assumption of ellipticity of the marginal distribution