Dear Nuno,
Least absolute residuals (LAR) — The LAR method finds a curve that minimizes the absolute difference of the residuals, rather than the squared differences. Therefore, extreme values have a lesser influence on the fit.
Bisquare weights — This method minimizes a weighted sum of squares, where the weight given to each data point depends on how far the point is from the fitted line. Points near the line get full weight. Points farther from the line get reduced weight. Points that are farther from the line than would be expected by random chance get zero weight. For most cases, the bisquare weight method is preferred over LAR because it simultaneously seeks to find a curve that fits the bulk of the data using the usual least-squares approach, and it minimizes the effect of outliers.
Also to make a summary:
- use LAR for data with less outliners/anomalies in your data. (each datapoint is as important as one other)
- use Bisquare for data which has outliners, but where you think that these outlines are due to i.e. disturbances and you don't want that your fit is affected by these outliners.
Kind regards, Christiaan van Ommeren
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