TRADE regression is a two-step reweighted least squares method. The name comes from TRim And DElete. The first step involves trimming of the residuals and it makes the method robust against outliers. And the second step (in which only extreme outliers are ignored) restores the statistical efficiency for normal errors.
During the last ten years the topic of high-breakdown methods is a very popular one among the developers of statistical methods. Some examples are Repeated Medians (Siegel, 1982), Least Median of Squares (Rousseeuw, 1984), S-estimators (Rousseeuw and Yohai, 1984), MM-estimators (Yohai, 1987) and τ-estimators (Yohai and Zamar, 1988). These very robust methods are extremely time-consuming and therefore only applicable for models with only a few variables. This is one of the reasons why they are not incorporated in the popular statistical packages.
TRADE regression is a compromise. The method is developed with the following objectives: (1) It must be applicable with the tools that are already present in packages like SAS, SPSS and BMDP, (2) It must be suitable for large datasets and (3) There should be a reasonable balance between robustness and statistical efficiency.
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