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 framework 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-called 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 established between the generalized rank annihilation method (GRAM) and the naive method by comparing expressions for prediction variance. The main conclusion is that the relatively poor efficiency of GRAM is the price one pays for obtaining the second-order advantage with a single calibration sample. Copyright (C) 2001 John Wiley & Sons, Ltd.
second-order advantage generalized rank annihilation method least squares prediction variance bilinear calibration