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Title: High-dimensional sufficient dimension reduction through principal projections Authors:  Andreas Artemiou - University of Limassol (Cyprus)
Eugen Pircalabelu - Université catholique de Louvain (Belgium) [presenting]
Abstract: A new dimension reduction method is presented for high-dimensional settings. The proposed procedure is based on a principal support vector machine framework where principal projections are used in order to overcome the non-invertibility of the covariance matrix. We show that one can accurately recover the central subspace using a projection on a lower dimensional subspace and then applying an l1 penalization strategy to obtain sparse estimators of the sufficient directions. Based next on a desparsified estimator, we provide an inferential procedure for high-dimensional models that allows testing for the importance of variables in determining the sufficient direction. Theoretical properties of the methodology are illustrated and computational advantages are demonstrated with simulated and real data experiments.