Abstract
In some multiple regression applications, the number of predictors has become large, and for this reason,the Sufficient Dimension Reduction (SDR) theory (Cook, 1998) has received much attention. The idea of SufficientDimension Reduction (SDR) is to replace X with a low-dimensional orthogonal projection on the subspaces ()without Loss of information about the distribution X without assuming any specific model. The target of the SDR isthe central subspace many methods have been worked out to find and one such method is the inverse regression (SIR)slices (Li, 1991). Applied in different fields, SIR has proven robust for dimension reduction (DR) approach and iseffective in handling high dimensional (HD) data and sufficient tools to deal with dimension reduction (DR) inconditional regression (Li and Yin, 2008). However, it does produce linear combinations (LCs) for all the originalpredictors. As a result, interpretation of SIR estimates can be difficult and sometimes misleading.This paper will use methods that combine SIR work with the Lasso method. Ni et al. (2005) A note on shrinkagesliced inverse regression (SH-SIR), Li and Yin (2008) Sliced Inverse Regression with Regularizations (RSIR) and Linet al.( (2018) Sparse Sliced Inverse Regression Via Lasso (SIR-L) methods in analysis sample data for high bloodpressure and the factors affecting it
