International Statistical Review

A Review of Envelope Models

Early View

Summary The envelope model was first introduced as a parsimonious version of multivariate linear regression. It uses dimension reduction techniques to remove immaterial variation in the data and has the potential to gain efficiency in estimation and improve prediction. Many advances have taken place since its introduction, and the envelope model has been applied to many contexts in multivariate analysis, including partial least squares, generalised linear models, Bayesian analysis, variable selection and quantile regression, among others. This article serves as a review of the envelope model and its developments for those who are new to the area.

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