Comments on construction of confidence intervals in connection with partial least squares

Faber and Kowalski recently proposed a method to calculate confidence regions for the regression coefficients in a linear model when partial least squares (PLS) has been used as an estimation method (J. Chemometrics, 11, 181 (1997)). In this short communication we show that the proposed confidence regions fail to have the correct coverage probability. The reason for this is that the PLS estimator is generally biased, whereas the method proposed by Faber and Kowalski requires an unbiased estimator. Similar objections made against PLS also apply to the second regression method mentioned by Faber and Kowalski, principal component regression (PCR).