Description
Book SynopsisSufficient dimension reduction is a rapidly developing research field that has wide applications in regression diagnostics, data visualization, machine learning, genomics, image processing, pattern recognition, and medicine, because they are fields that produce large datasets with a large number of variables. Sufficient Dimension Reduction: Methods and Applications with R introduces the basic theories and the main methodologies, provides practical and easy-to-use algorithms and computer codes to implement these methodologies, and surveys the recent advances at the frontiers of this field.
Features
- Provides comprehensive coverage of this emerging research field.
- Synthesizes a wide variety of dimension reduction methods under a few unifying principles such as projection in Hilbert spaces, kernel mapping, and von Mises expansion.
- Reflects most recent advances such as nonlinear sufficient dimension re
Trade Review
"...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
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
