History and Unpopularity of Robust Regression
Despite their superior performance over least squares estimation in many situations, robust methods for regression are still not widely used. Several reasons may help explain their unpopularity (Hampel et al. 1986, 2005). One possible reason is that there are several competing methods and the field got off to many false starts. Also, computation of robust estimates is much more computationally intensive than least squares estimation; in recent years however, this objection has become less relevant as computing power has increased greatly. Another reason may be that some popular statistical software packages failed to implement the methods (Stromberg, 2004). The belief of many statisticians that classical methods are robust may be another reason.
Although uptake of robust methods has been slow, modern mainstream statistics text books often include discussion of these methods (for example, the books by Seber and Lee, and by Faraway; for a good general description of how the various robust regression methods developed from one another see Andersen's book). Also, modern statistical software packages such as R, Stata and S-PLUS include considerable functionality for robust estimation (see, for example, the books by Venables and Ripley, and by Maronna et al.).
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