We describe and elaborate on foundations that connect partial least squares regression with recently developed envelope theory and methodology. These foundations explain why PLS regression can work well in high-dimensional regressions where the number of predictors exceeds the number of observations and set it apart from other predictive methodologies. We hope that our foundational perspective will stimulate cross-fertilization between statistics and chemometrics, leading eventually to important methodological advancements.
- SIMPLS algorithm
- abundant regressions
- high-dimensional regressions
- sparse regressions
- sufficient dimension reduction