Statistics for High-Dimensional Data Methods, Theory and Applications [Hardcover]

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.

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.

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.

From the reviews:

This book is a complete study of ₁-penalization based statistical methods for high-dimensional data & . Definitely, this book is useful. & its strong level in mathematics makes it more suitable to researchers and graduate students who already have a strong background in statistics. &lSÃ