Large outliers break down linear and nonlinear regression models. Robust
regression methods allow one to filter out the outliers when building a model.
By replacing the traditional least squares criterion with the least trimmed
squares criterion, in which half of data is treated as potential outliers, one
can fit accurate regression models to strongly contaminated data.
High-breakdown methods have become very well established in linear regression,
but have started being applied for non-linear regression only recently.