Partial Least Squares Estimator for Single-index Models
Journal of the Royal Statistical Society, 2000

The partial least squares (PLS) approach first constructs new explanatory variables, known as factors (or components), which are linear combinations of available predictor variables. A small subset of these factors is then chosen and retained for prediction.

Professors Prasad Naik and Chih-Ling Tsai study the performance of PLS in estimating single-index models, especially when the predictor variables exhibit high collinearity. The authors show that PLS estimates are consistent up to a constant of proportionality. They present three simulations studies that compare the performance of PLS in estimating single-index models with that of sliced inverse regression (SIR).