Big data and partial least-squares prediction

We give a 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 → ∞ 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→ ∞ These results support the conjecture that PLS regression can be an effective method for prediction in big high-dimensional regressions.