Outlier-resistant errors-in-variables regression: anomaly recognition and grain-size correction in stream sediments

Regression analysis is a well-established method to correct for grain size differences in suites of sediments. However, distortion caused by the presence of outliers and imprecision in both variables can hinder many common regression models from performing adequately. Median sum of weighted residuals (MSWR) regression is strongly outlier-resistant and accounts for imprecision in both variables for each member of a dataset. In a case study of Ni and Pb normalisation for a suite of stream sediments in NE Estonia, the ability of MSWR regression to detect anomalies was compared to ordinary least squares, weighted least squares, least absolute deviation and least median of squares regression. MSWR regression not only revealed more anomalous samples than the other methods, but also was able to distinguish anomalies in samples at comparatively low heavy metal concentration. This feature is particularly significant when tracking heavy metal dispersion downstream from point sources.