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Estimation Errors of Component Spectra Estimated by Means of the Concentration-Spectrum Correlation: Part II

Volume 43, Number 5 (July 1989) Page 855-860

Uozumi, Jun; Asakura, Toshimitsu

Estimation errors accompanying component spectra calculated by means of the concentration-spectrum correlation method are investigated by theoretical analysis and computer simulations. Discussion is concentrated on a modified version of the method, which operates under the constraint that the sum of all the component concentrations in a sample is unity. In an agreement similar to that for the basic method, which was treated in an earlier paper [Appl. Spectrosc. 43, 74 (1989)], the estimation error consists of a superposition of other component spectra, each multiplied by a weighting factor. In this case, however, the weighting factor is a function of five sample statistics: the averages and the standard deviations of the concentrations of both the objective and the interfering components, and the correlation coefficient of these two components. It is shown again that the nonparametric statistical technique called a bootstrap is useful as a tool of false-true discrimination of the peaks in the estimated spectra.