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.
Author(s): Peter Bühlmann, Sara van de Geer (auth.)
Series: Springer Series in Statistics
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Language: English
Pages: 558
Tags: Statistical Theory and Methods; Probability and Statistics in Computer Science
Front Matter....Pages i-xvii
Introduction....Pages 1-6
Lasso for linear models....Pages 7-43
Generalized linear models and the Lasso....Pages 45-53
The group Lasso....Pages 55-76
Additive models and many smooth univariate functions....Pages 77-97
Theory for the Lasso....Pages 99-182
Variable selection with the Lasso....Pages 183-247
Theory for ℓ 1 /ℓ 2 -penalty procedures....Pages 249-291
Non-convex loss functions and ℓ 1 -regularization....Pages 293-338
Stable solutions....Pages 339-358
P-values for linear models and beyond....Pages 359-386
Boosting and greedy algorithms....Pages 387-431
Graphical modeling....Pages 433-480
Probability and moment inequalities....Pages 481-538
Back Matter....Pages 539-556
