GENERALIZED RANK ANNIHILATION METHOD - STANDARD ERRORS IN THE ESTIMATED EIGENVALUES IF THE INSTRUMENTAL ERRORS ARE HETEROSCEDASTIC AND CORRELATED

The generalized rank annihilation method (GRAM) is a method for curve resolution and calibration that uses two data matrices simultaneously, i.e. one for the unknown and one for the calibration sample. The meth od is known to become an eigenvalue problem for which the eigenvalues are the ratios of the concentrations for the samples under scrutiny. P reviously derived standard errors in the estimated eigenvalues of GRAM have very recently been shown to be based on unrealistic assumptions about the measurement errors. In this paper a systematic notation is i ntroduced that enables the propagation of errors that are based on rea listic assumptions concerning the data-generating process. The error p ropagation will be performed in detail for the case that one data orde r modulates the second one. Extensions to more complicated error model s are indicated. (C) 1997 by John Wiley & Sons, Ltd.