Statistics for High-Dimensional Data

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2013
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	576
Reihe:	Springer Series in Statistics
Inhalt:	xviii 558 S.
ISBN-13:	9783642268571
ISBN-10:	3642268579
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	de Geer, Sara van Bühlmann, Peter
Auflage:	2011
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Springer Series in Statistics
Maße:	235 x 155 x 31 mm
Von/Mit:	Sara van de Geer (u. a.)
Erscheinungsdatum:	03.08.2013
Gewicht:	0,861 kg

preigu-id: 105702640