Bing Li

Sufficient Dimension Reduction (eBook, PDF)

Methods and Applications with R

• Format: PDF

Produktbeschreibung

Sufficient dimension reduction was first introduced in the early 90's as a set of graphical and diagnostic tools for regression with many predictors. Over the past two decades or so it has developed into a powerful theory and technique for handling high-dimensional data. This book will introduce the main results and important techniques in this area, and explore the current frontiers of research. These will be accompanied by numerical studies, data analysis, and computer codes.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 304
• Erscheinungstermin: 27. April 2018
• Englisch
• ISBN-13: 9781498704489
• Artikelnr.: 56834224

Autorenporträt

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.

Inhaltsangabe

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

Rezensionen

"...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