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Partial least squares estimator for single‐index models

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. We study the performance of PLS in estimating single‐index models, especially when the predictor variables exhibit high collinearity. We show that PLS estimates are consistent up to a constant of proportionality. We present three simulation studies that compare the performance of PLS in estimating single‐index models with that of sliced inverse regression (SIR). In the first two studies, we find that PLS performs better than SIR when collinearity exists. In the third study, we learn that PLS performs well even when there are multiple dependent variables, the link function is non‐linear and the shape of the functional form is not known.