Generalized rank annihilation method: standard errors in the estimated eigenvalues if the instrumental errors are heteroscedastic and correlated
✍ Scribed by Klaas Faber; Avraham Lorber; Bruce R. Kowalski
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 195 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0886-9383
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✦ Synopsis
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 datagenerating 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.