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 …

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Aiming at abundant scientific and engineering data with not only high dimensionality but
also complex structure, we study the regression problem with a multidimensional array …

We review probabilistic principal components, principal fitted components, sufficient
dimension reduction, and envelopes, arguing that at their core they are all based on …

We build connections between envelopes, a recently proposed context for efficient
estimation in multivariate statistics, and multivariate partial least squares (PLS) regression …

Envelopes were recently proposed by Cook, Li and Chiaromonte as a method for reducing
estimative and predictive variations in multivariate linear regression. We extend their …

Modern technology often generates data with complex structures in which both response
and explanatory variables are matrix valued. Existing methods in the literature can tackle …

Statistics is the science of extracting useful information from data, and a statistical model is
used to provide a useful approximation to some of the important characteristics of the …

Sparse partial least squares (SPLS) is widely used in applied sciences as a method that
performs dimension reduction and variable selection simultaneously in linear regression …

A Bayesian approach for envelope models Page 1 The Annals of Statistics 2017, Vol. 45, No.
1, 196–222 DOI: 10.1214/16-AOS1449 © Institute of Mathematical Statistics, 2017 A …