A selective overview of sparse sufficient dimension reduction

Abstract

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.

Keywords:

• Minimax rate
• sparse sufficient dimension reduction
• variable selection
• variable screening

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by the National Natural Science Foundation of China Grant 11971170, the 111 project B14019 and the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning.

Notes on contributors

Lu Li

Lu Li is currently a Ph.D student at School of Statistics, East China Normal University.

Xuerong Meggie Wen

Dr Xuerong Meggie Wen is currently an associate professor of Statistics at Dept. of Mathematics and Statistics, Missouri University of Science and Technology.

Zhou Yu

Dr Zhou Yu is a Professor of Statistics at School of Statistics, East China Normal Univercity.