Statistics for high-dimensional data: methods, theory and applications

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, andprocedures controlling false positive selections. A special characteristic ofthe 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. 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. INDICE: 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. Stablesolutions. 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.

• ISBN: 978-3-642-20191-2
• Editorial: Springer Berlin Heidelberg
• Encuadernacion: Cartoné
• Páginas: 556
• Fecha Publicación: 01/05/2011
• Nº Volúmenes: 1
• Idioma: Inglés