A selective overview of sparse sufficient dimension reduction

High-dimensional data analysis has been a challenging issue in statistics. Sufficient dimension reduction aims to reduce the dimension of the predictors by replacing the original predictors with a minimal set of their linear combinations without loss of information. However, the estimated linear combinations generally consist of all of the variables, making it difficult to interpret. To circumvent this difficulty, sparse sufficient dimension reduction methods were proposed to conduct model-free variable selection or screening within the framework of sufficient dimension reduction. We review the current literature of sparse sufficient dimension reduction and do some further investigation in this paper.