Statistics for High-Dimensional Data

Statistics for High-Dimensional Data
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Methods, Theory and Applications
 eBook
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Artikel-Nr:
9783642201929
Veröffentl:
2011
Einband:
eBook
Seiten:
558
Autor:
Peter Bühlmann
Serie:
Springer Series in Statistics
eBook Typ:
PDF
eBook Format:
Reflowable eBook
Kopierschutz:
Digital Watermark [Social-DRM]
Sprache:
Englisch
Beschreibung:

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.

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.

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.

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