Bootstrapping principal component regression models

Bootstrap methods can be used as an alternative for cross-validation in regression procedures such as principal component regression (PCR). Several bootstrap methods for the estimation of prediction errors and confidence intervals are presented. It is shown that bootstrap error estimates are consistent with cross-validation estimates but exhibit less variability. This makes it easier to select the correct number of latent variables in the model. Using bootstrap confidence intervals for the regression vectors, it is possible to select a subset of the original variables to include in the regression, yielding a more parsimonious model with smaller prediction errors. The methods are illustrated using PCR, but can be applied to all regression models yielding a vector or matrix of regression coefficients. (C) 1997 by John Wiley & Sons, Ltd.