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 …

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

We review sufficient dimension reduction (SDR) estimators with multivariate response in this
paper. A wide range of SDR methods are characterized as inverse regression SDR …

Abstract The Minimum Average Variance Estimation (MAVE) method and its variants have
proven to be effective approaches to the dimension reduction problems. However, as far as …

In this paper, we focus on partial dimension reduction for conditional mean function in the
presence of controlling variable when responses are multivariate and missing at random. A …

Multivariate response data often arise in practice and they are frequently subject to
missingness. Under this circumstance, the standard sufficient dimension reduction (SDR) …

In this paper, we are concerned with nonlinear interaction detection based on partial
dimension reduction with missing response data. The covariates are grouped through linear …

Researchers often need to infer how the conditional mean of a response varies with the
predictors. Sufficient dimension-reduction techniques reduce the dimension by identifying a …

In this paper we propose an efficient model-based sufficient dimension reduction method to
detect interactions. We introduce a new class of multivariate adaptive varying index models …

In the two-stage LOFTS procedure, the first-stage screening performance is crucial for the
follow-up test according to Theorem 1. Thus, we first examine whether all the truly important …