© 2011

Statistics for High-Dimensional Data

Methods, Theory and Applications


  • Contains the fundamentals of the recent research in a very timely area

  • Gives an overview of the area and adds many new insights

  • There is a unique mix of methodology, theory, algorithms and applications

  • The number of recent papers on the topic is huge

  • Is a welcome consolidation

  • Is an essential for the further development of theory and methods


Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Peter Bühlmann, Sara van de Geer
    Pages 1-6
  3. Peter Bühlmann, Sara van de Geer
    Pages 7-43
  4. Peter Bühlmann, Sara van de Geer
    Pages 45-53
  5. Peter Bühlmann, Sara van de Geer
    Pages 55-76
  6. Peter Bühlmann, Sara van de Geer
    Pages 77-97
  7. Peter Bühlmann, Sara van de Geer
    Pages 99-182
  8. Peter Bühlmann, Sara van de Geer
    Pages 183-247
  9. Peter Bühlmann, Sara van de Geer
    Pages 249-291
  10. Peter Bühlmann, Sara van de Geer
    Pages 293-338
  11. Peter Bühlmann, Sara van de Geer
    Pages 339-358
  12. Peter Bühlmann, Sara van de Geer
    Pages 359-386
  13. Peter Bühlmann, Sara van de Geer
    Pages 387-431
  14. Peter Bühlmann, Sara van de Geer
    Pages 433-480
  15. Peter Bühlmann, Sara van de Geer
    Pages 481-538
  16. Back Matter
    Pages 539-556

About this book


Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections.
A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.


L1-regularization algorithms oracle inequalities sparsity variable and feature selection

Authors and affiliations

  1. 1., Department of MathematicsSeminar for StatisticsZürichSwitzerland
  2. 2.ZürichSwitzerland

About the authors

Peter Bühlmann is Professor of Statistics at ETH Zürich. His main research areas are high-dimensional statistical inference, machine learning, graphical modeling, nonparametric methods, and statistical modeling in the life sciences. He is currently editor of the Annals of Statistics. He was awarded a Medallion lecture by the Institute of Mathematical Statistics in 2009 and read a paper to the Royal Statistical Society in 2010.

Sara van de Geer has been a full professor at the ETH in Zürich since 2005. Her main areas of research are empirical process theory, statistical learning theory, and nonparametric and high-dimensional statistics. She is an associate editor of Probability Theory and Related Fields, The Scandinavian Journal of Statistics and Statistical Surveys and a member of the Swiss National Science Foundation and correspondent of the Dutch Royal Academy of Sciences.
She received the IMS medal in 2003 and the ISI award in 2005, and was an invited speaker at the International Conference of Mathematicians in 2010.

Bibliographic information

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From the reviews:

“This book is a complete study of ℓ1-penalization based statistical methods for high-dimensional data … . Definitely, this book is useful. … its strong level in mathematics makes it more suitable to researchers and graduate students who already have a strong background in statistics. … it gives the state-of-the-art of the theory, and therefore can be used for an advanced course on the topic. … the last part of the book is an exciting introduction to new research perspectives provided by ℓ1-penalized methods.” (Pierre Alquier, Mathematical Reviews, Issue 2012 e)

“All Classical Statisticians interested in the very popular but a bit old methodologies like the Lasso (Tibshirani, 1996), its modifications like adaptive Lasso (Zou, 2006), and their theory, computational algorithms, applications to bioinformatics and other high dimensional applications. All such researchers would find this book worth buying. It is written by two outstanding theoreticians with flair for clear writing and excellent applications. … theory depends a lot on new concentration inequalities coming from the French probabilists. The book has good collection of these, with proofs.” (Jayanta K. Ghosh, International Statistical Review, Vol. 80 (3), 2012)