Iteratively reweighted generalized rank annihilation method 1. Improved handling of prediction bias

The generalized rank annihilation method (CRAM) is a method for curve resol ution and calibration that uses two bilinear matrices simultaneously, i.e., one for the unknown and one for the calibration sample. A GRAM calculation amounts to solving an eigenvalue problem for which the eigenvalues are rel ated to the predicted analyte concentrations. Previous studies have shown t hat random measurement errors bring about a bias in the eigenvalues, which directly translates into prediction bias. In this paper, accurate formulas are derived that enable removing most of this bias. Two bias correction met hods are investigated. While the first method directly subtracts bias from the eigenvalues obtained by the original GRAM, the second method first appl ies a weight to the data matrices to reduce bias. These weights are specifi c for the analyte of interest and must be determined iteratively from the d ata. Consequently, the proposed modification is called iteratively reweight ed GRAM (IRGRAM). The results of Monte Carlo simulations show that both met hods are effective in the sense that the standard error in the bias-correct ed prediction compares favourably with the root mean squared error (RMSE) t hat accompanies the original quantity. However, IRGRAM is found to perform best because the increase of variance caused by subtracting bias is minimis ed, In the original formulation of GRAM only a single calibration sample is exploited. The error analysis is extended to cope with multiple calibratio n samples. (C) 2001 Elsevier Science B.V. All rights reserved.