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Statistics for High-Dimensional Data Peter Buhlmann

Statistics for High-Dimensional Data By Peter Buhlmann

Statistics for High-Dimensional Data by Peter Buhlmann


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Summary

This valuable compendium of statistical methods features a unique combination of methodology, theory, algorithms and applications. It covers recently developed approaches to handling large and complex data sets, including the Lasso and boosting methods.

Statistics for High-Dimensional Data Summary

Statistics for High-Dimensional Data: Methods, Theory and Applications by Peter Buhlmann

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.

Statistics for High-Dimensional Data Reviews

From the reviews:

"This book is a complete study of 1-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 1-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)

About Peter Buhlmann

Peter Buhlmann is Professor of Statistics at ETH Zurich. 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 Zurich 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.

Table of Contents

Introduction.- Lasso for linear models.- Generalized linear models and the Lasso.- The group Lasso.- Additive models and many smooth univariate functions.- Theory for the Lasso.- Variable selection with the Lasso.- Theory for l1/l2-penalty procedures.- Non-convex loss functions and l1-regularization.- Stable solutions.- P-values for linear models and beyond.- Boosting and greedy algorithms.- Graphical modeling.- Probability and moment inequalities.- Author Index.- Index.- References.- Problems at the end of each chapter.

Additional information

NLS9783642268571
9783642268571
3642268579
Statistics for High-Dimensional Data: Methods, Theory and Applications by Peter Buhlmann
New
Paperback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
2013-08-03
558
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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