Envelopes and Partial Least Squares Regression

• Activity Number: 57
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Zhihua Su*+ and Dennis Cook and Inge Helland
• Companies: and University of Minnesota and University of Oslo
• Keywords: Dimension reduction ; Envelope models ; Partial least squares ; SIMPLS algorithm

Abstract

We build connections between envelopes, a recently proposed context for efficient estimation in multivariate statistics, and multivariate partial least squares (PLS) regression. In particular, we establish an envelope as the nucleus of both univariate and multivariate PLS, which opens the door to pursuing the same goals as PLS but using different envelope estimators. It is argued that a likelihood-based envelope estimator is less sensitive to the number of PLS components selected and that it outperforms PLS in prediction and estimation.