Abstract
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــAbstract: The SDR (sufficient dimension reduction) is one of the important topics in many scientific fields. It has attracted attention of researchers because it is considered a beneficial approach to address the problem of the high dimension HD that has emerged due to the explosion of large data in the last decades. Under SDR framework settings, many procedures are proposed to combine the ideas of SDR methods and regularization approaches. In this paper, we present some of these methods, the SMAVE-EN (sparse MAVE - elastic net), RSMAVE (robust sparse MAVE) and RSMAVE-EN (robust sparse MAVE - elastic net). Also, the diabetic data are analyzed through the mentioned methods.