Robust regression techniques A useful alternative for the detection of outlier data in chemical analysis

The validation of an analytical procedure means the evaluation of some performance criteria such as accuracy, sensitivity, linear range, capability of detection, selectivity, calibration curve, etc. This implies the use of different statistical methodologies, some of them related with statistical regression techniques, which may be robust or not. The presence of outlier data has a significant effect on the determination of sensitivity, linear range or capability of detection amongst others, when these figures of merit are evaluated with non-robust methodologies. In this paper some of the robust methods used for calibration in analytical chemistry are reviewed: the Huber M-estimator; the Andrews, Tukey and Welsh GM-estimators; the fuzzy estimators; the constrained M-estimators, CM; the least trimmed squares, LTS. The paper also shows that the mathematical properties of the least median squares (LMS) regression can be of great interest in the detection of outlier data in chemical analysis. A comparative analysis is made of the results obtained by applying these regression methods to synthetic and real data. There is also a review of some applications where this robust regression works in a suitable and simple way that proves very useful to secure an objective detection of outliers. The use of a robust regression is recommended in ISO 5725-5.