Big Data and Partial Least-Squares Prediction

• Activity Number: 319 - Highlights of the Canadian Journal of Statistics
• Type: Invited
• Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Dennis Cook* and Liliana Forzani
• Companies: University of Minnesota and Departamento de Matematica, Universidad Nacional del Litoral

Abstract

We give a brief commentary on the challenges of big data for Statistics. We then narrow our discussion to one of those challenges: dimension reduction. This leads to consideration of one particular dimension reduction method—partial least-squares (PLS) regression—for prediction in big high-dimensional regressions where the sample size and the number of predictors are both large. We show that in some regression contexts single-component PLS predictions converge at the usual root-n rate as (n, p) go to infinity regardless of the relationship between the sample size n and number of predictors p. Asymptotically, PLS predictions then behave as regression predictions in the usual context where p is fixed and n goes to infinity. These results support the conjecture that PLS regression can be an effective method for prediction in big high-dimensional regressions.