Statistics for high-dimensional data: methods, theory and applications
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 m…
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- Full title :Statistics for high-dimensional data : methods, theory and applications / Peter Bühlmann, Sara van de Geer.
Summary
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.
Read More ↓Edition Statements
- Publication Date:©2011.
Publication Statements
- Publisher(s):Springer
- Place of Publication:Heidelberg
- Language:eng
- Publication Date:©2011.
The Physical Object
- Description:xvii, 556 pages : : illustrations (some color) ; : 24 cm.
Edition Identifiers
- ISBN:9783642201912, 3642201911
- oclc:ocn729346867
- LC Classification:QA276
- Dewey Decimal:519.5
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-regulation -- Stable solutions -- P-values for linear models and beyond -- Boosting and greedy algorithms -- Graphical modeling -- Probabililty and moment inequalities.
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