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Generalized rank annihilation method: standard errors in the estimated eigenvalues if the instrumental errors are heteroscedastic and correlated
Author(s) -
Faber Klaas,
Lorber Avraham,
Kowalski Bruce R.
Publication year - 1997
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/(sici)1099-128x(199703)11:2<95::aid-cem454>3.0.co;2-m
Subject(s) - eigenvalues and eigenvectors , rank (graph theory) , mathematics , propagation of uncertainty , heteroscedasticity , notation , calibration , standard error , annihilation , algorithm , statistics , arithmetic , combinatorics , physics , quantum mechanics
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 method is known to become an eigenvalue problem for which the eigenvalues are the ratios of the concentrations for the samples under scrutiny. Previously 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 introduced that enables the propagation of errors that are based on realistic assumptions concerning the data‐generating process. The error propagation will be performed in detail for the case that one data order modulates the second one. Extensions to more complicated error models are indicated. © 1997 John Wiley & Sons, Ltd.