Written by the leading expert in the field, this text reviews the major new developments in envelope models and methods

An Introduction to Envelopes provides an overview of the theory and methods of envelopes, a class of procedures for increasing efficiency in multivariate analyses without altering traditional objectives. The author offers a balance between foundations and methodology by integrating illustrative examples that show how envelopes can be used in practice. He discusses how to use envelopes to target selected coefficients and explores predictor envelopes and their connection with partial least squares regression. The book reveals the potential for envelope methodology to improve estimation of a multivariate mean.

The text also includes information on how envelopes can be used in generalized linear models, regressions with a matrix-valued response, and reviews work on sparse and Bayesian response envelopes. In addition, the text explores relationships between envelopes and other dimension reduction methods, including canonical correlations, reduced-rank regression, supervised singular value decomposition, sufficient dimension reduction, principal components, and principal fitted components. This important resource:

- Offers a text written by the leading expert in this field

- Describes groundbreaking work that puts the focus on this burgeoning area of study

- Covers the important new developments in the field and highlights the most important directions

- Discusses the underlying mathematics and linear algebra

- Includes an online companion site with both R and Matlab support

Written for researchers and graduate students in multivariate analysis and dimension reduction, as well as practitioners interested in statistical methodology, An Introduction to Envelopes offers the first book on the theory and methods of envelopes.

Partial least squares (PLS) regression is, at its historical core, a black-box algorithmic method for dimension reduction and prediction based on an underlying linear relationship between a possibly vector-valued response and a number of predictors.

Through envelopes, much more has been learned about PLS regression, resulting in a mass of information that allows an envelope bridge that takes PLS regression from a black-box algorithm to a core statistical paradigm based on objective function optimization and, more generally, connects the applied sciences and statistics in the context of PLS. This book focuses on developing this bridge. It also covers uses of PLS outside of linear regression, including discriminant analysis, non-linear regression, generalized linear models and dimension reduction generally.

Key Features:

- Showcases the first serviceable method for studying high-dimensional regressions.

- Provides necessary background on PLS and its origin.

- R and Python programs are available for nearly all methods discussed in the book.

This book can be used as a reference and as a course supplement at the Master's level in Statistics and beyond. It will be of interest to both statisticians and applied scientists.

Mit Hilfe der Regressionsanalyse versucht man, einen Zusammenhang zwischen einer Systemantwort und einer oder mehreren bestimmenden Variablen zu finden. In den letzten Jahren wurden einige neue Regressionsverfahren entwickelt, die dieses Buch behandelt und - mit der graphischen Analyse als bergeordnetem Aspekt - vergleicht. (10/99)

Zur graphischen Pr sentation von Regressionsdaten gibt es seit dem Vormarsch der Computertechnik vielf ltige neue M glichkeiten, die ber die klassischen Ans tze hinausgehen. Der Autor betritt mit seinen Ideen h ufig Neuland; er illustriert sie mit zahlreichen Beispielen, Diagrammen und Abbildungen (die entsprechenden 3D- und Farbversionen sind ber Internet abrufbar). (11/98)