The price paid for the second-order advantage when using the generalized rank annihilation method (GRAM)

In a ground-breaking paper, Linder and Sundberg developed a statistical fra mework for the calibration of bilinear data (Chemometrics Intell. Lab. Syst . 1998; 42: 159-178). Within this framework they formulated three different predictor construction methods (J. Chemometrics accepted), namely a so-cal led naive method, a least squares (LS) method and a refined version of the latter that takes account of the calibration uncertainty. They showed that the naive method is statistically less efficient than the others under the assumption of white noise. In the current work a close relationship is esta blished between the generalized rank annihilation method (GRAM) and the nai ve method by comparing expressions for prediction variance. The main conclu sion is that the relatively poor efficiency of GRAM is the price one pays f or obtaining the second-order advantage with a single calibration sample. C opyright (C) 2001 John Wiley & Sons, Ltd.