Sufficient Dimension Reduction: Methods and Applications with R (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

Bing Li



Sufficient 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.













  • 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 reduction, dimension folding for tensorial data, as well as sufficient dimension reduction for functional data.
  • Includes a set of computer codes written in R that are easily implemented by the readers.
  • Uses real data sets available online to illustrate the usage and power of the described methods.


Sufficient dimension reduction has undergone momentous development in recent years, partly due to the increased demands for techniques to process high-dimensional data, a hallmark of our age of Big Data. This book will serve as the perfect entry into the field for the beginning researchers or a handy reference for the advanced ones.


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.




- 提供了對這一新興研究領域的全面覆蓋。
- 在幾個統一原則下綜合了各種降維方法,如希爾伯特空間中的投影、核映射和馮·米塞斯展開。
- 反映了非線性充分降維、張量數據的降維折疊以及函數數據的充分降維等最新進展。
- 包含一組用R編寫的計算機代碼,讀者可以輕鬆實現。
- 使用在線上可用的真實數據集來說明所描述方法的使用和能力。


Bing Li在芝加哥大學獲得博士學位,目前是賓夕法尼亞州立大學的統計學教授。他的研究興趣包括充分降維、統計圖模型、函數數據分析、機器學習、估計方程和拟似似然、以及魯棒統計。他是數學統計學會和美國統計學會的會士,是《統計學年鑒》和《美國統計學會期刊》的副編輯。