Partial Least Square: Theoretical Results for the Chemometrics Use of PLS

• Activity Number: 56 - Novel Statistical Methods for Variable Selection with Applications
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2018 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Liliana Forzani* and Dennis Cook
• Companies: FACULTAD DE INGENIERIA QUIMICA and School of Statistics
• Keywords: partial least square; p larger than n

Abstract

Partial least squares (PLS) is one of the first methods for prediction in high-dimensional linear regressions in which the sample size need not be large relative to the number of predictors. Since its development, PLS regression has taken place mainly within the chemometrics community, where empirical prediction is the main issue, but PLS is now a core method for big data. However, studies of PLS have appeared in mainline statistics literature only from time to time and there have been no positive results on the theoretical properties of the chemometrics community's use of PLS. In a joint work with R. Dennis Cook we study the theoretical properties of prediction using PLS in the same context that chemometrics community use.