Envelopes and Related Paradigms for Dimension and Rank Reduction in Regression

• Activity Number: 87 - Reduced-Rank Methods: Seventy Years of History and State-of-the-Art Developments
• Type: Invited
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Dennis Cook*
• Companies: University of Minnesota
• Keywords: sufficient dimension reduction; reduced rank regression; partial least squares; principal components

Abstract

We describe how selected dimension and rank reduction strategies are connected conceptually, paving the way for a unified view of multivariate dimension reduction and leading to contemporary methods like envelopes. Specific paradigms covered include envelopes, sufficient dimension reduction, reduced rank regression, and partial least squares. Emphasis will be given to underlying motifs and how they form a conceptual foundation for these and other paradigms.