Treatment of Model Error in Calibration by Robust and Fuzzy Procedures

Abstract

In every mathematical (e.g., statistical) procedure and theorem used in calibration, several conditions need to be fulfilled. What can analysts and chemometricians do, however, if the conditions are only nearly fulfilled? One can expect that small changes in the conditions yield only small changes in the results. This article shows how to treat two types of model error caused by assuming an incorrect error distribution or relationship (i.e., linear). The procedures applied are based on robust statistics and fuzzy theory, respectively.

A New Fuzzy Regression Algorithm

“…Illustrative Example 1. To illustrate the characteristics of performance of the fuzzy regression algorithm (FR) in the case of small deviations from homoscedasticity or in the presence of outliers, we refer to the data discussed by Rajkó, concerning the determination by ICP-AES of Mo, Cr, Co, Pb, and Ni in subsurface and drinking water (Table ).…”

“…There are several reasons why data may be discrepant, a gross measurement error being the most obvious one. Another is the fact that certain data points may be particularly sensitive to some unmodeled (or unadequately modeled) parameter or, from another point of view, particularly sensitive to some systematic error that has not been accounted for in the experiment …”

Application of SIC (simple interval calculation) for object status classification and outlier detection—comparison with regression approach

“…The SIC interval stands in contrast to the more traditional confidence interval estimators based upon theoretical error distributional model assumptions, which certainly do not always hold for practical data analysis of real-world technological and natural systems anyway [23].…”