Statistics for high-dimensional data methods, theory and applications - Bühlmann, Peter; Geer, S. A. van de (Sara A.) (Heidelberg, Germany Springer Berlin, 2011)
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-regulation -- Stable solutions -- P-values for linear models and beyond -- Boosting and greedy algorithms -- Graphical modeling -- Probabililty and moment inequalities
Keywords: Mathematical statistics; Smoothness of functions; Nonconvex programming; Least absolute deviations (Statistics); Linear models (Statistics)