Table of Contents

1. Dimension Reduction Subspaces 2. Sliced Inverse Regression 3. Parametric and Kernel Inverse Regression 4. Sliced Average Variance Estimate 5. Contour Regression and Directional Regression 6. Elliptical Distribution and Transformation of Predictors 7. Sufficient Dimension Reduction for Conditional Mean 8. Asymptotic Sequential Test for Order Determination 9. Other Methods for Order Determination 10. Forward Regressions for Dimension Reduction 11. Nonlinear Sufficient Dimension Reduction 12. Generalized Sliced Inverse Regression 13. Generalized Sliced Average Variance Estimator

About the Author

Bing Li obtained his Ph.D. from the University of Chicago. He is currently a Professor of Statistics at the Pennsylvania State University. His research interests cover sufficient dimension reduction, statistical graphical models, functional data analysis, machine learning, estimating equations and quasilikelihood, and robust statistics. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association. He is an Associate Editor for The Annals of Statistics and the Journal of the American Statistical Association.

Reviews

"...Sufficient Dimension Reduction: Methods and Applications with R is a thorough overview of the key ideas and a detailed reference for advanced researchers...Professor Li gives careful discussions of the relevant details, rendering the text impressively self-contained. But as one would expect from a book based on graduate course notes, this manuscript is mainly accessible to those with advanced training in theoretical statistics...This book serves as an excellent introduction to the field of sufficient dimension reduction, and the depth of presentation and theoretical rigor are impressive. It would, of course, naturally serve as the basis for a deep graduate course, and provides a substantial foundation for anyone hoping to contribute in this thriving area."
- Daniel J. McDonald, JASA 2020