Comparison of robust regression methods based on least-median and adaptive kalman filtering approaches applied to linear calibration data

Five algorithms for data analysis are evaluated for their abilities to discriminate against outliers in small data sets (4-10 points). These methods included least-squares regression, the least absolute -deviation method, the least median of squares method, and two techniques based on an adaptive Kalman filter. For data sets consisting of 4-9 points with one outlier, the average errors in the estimation of the slope were found to be 18.9 % by least-squares, 17.7% by the least absolute deviation method, 0.5% by the least median of squares algorithm, 9.1% by an adaptive Kalman filter algorithm, and 0.9% by a zero-lag adaptive Kalman filter algorithm. Based on these results, the conclusion is that the zero-lag adaptive Kalman filter and the least median of squares approaches are best suited for the detection of outliers in small calibration data sets.