Last modified Dec. 21, 1999 by fkc
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Decomposition of absorption spectra using linear regression has been
proposed for calculating concentrations of mixture compounds. The
method is based on projecting the observed mixture spectrum onto the
linear space generated by the reference spectra that correspond to
the individual components comprising the mixture. The computed
coefficients are then used as estimates for concentration of the
components that comprise the mixture. Existence of unknown
components in the mixture, however, introduces bias on the obtained
concentration estimates. We extend the usual linear regression model
to an additive semi-parametric model to take the unknown component
into account, estimate the absorption profile of the unknown
component, and obtain concentration estimates of the known
compounds. A standard back-fitting method as well as a mean
weighted least squares criterion are applied. The techniques are
illustrated on simulated absorption spectra.
KEYWORDS:
Parameter estimation, non-parametric methods, unbiased estimates,
chemometry, absorption spectra, additive models, semi-parametric
models, mean weighted least squares, back-fitting.