Bühlmann, Peter.

Statistics for High-Dimensional Data Methods, Theory and Applications / [electronic resource] : by Peter Bühlmann, Sara van de Geer. - XVIII, 558 p. online resource. - Springer Series in Statistics, 0172-7397 . - Springer Series in Statistics, .

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.

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.


10.1007/978-3-642-20192-9 doi

Mathematical statistics.
Statistical Theory and Methods.
Probability and Statistics in Computer Science.



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