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. Chemome trics, 11, 181 (1997)). In this short communication we show that the p roposed confidence regions fail to have the correct coverage probabili ty. The reason for this is that the PLS estimator is generally biased, whereas the method proposed by Faber and Kowalski requires an unbiase d estimator. Similar objections made against BLS also apply to the sec ond regression method mentioned by Faber and Kowalski, principal compo nent regression (PCR). (C) 1998 John Wiley & Sons, Ltd.