RE: Summary of Robust Regression Algorithms

David Ross (ross@math.hawaii.edu)
Tue, 6 Jan 98 11:05:26 HST


Recently I posted a simple example of how a 'robust' method (simple
median) can seem non-robust. This was a bit of a troll; most respondants
have characterized the example as pathological, or
model-inappropropriate, or not relevant to practice. Now, let me refer
you to a little paper by Hettmansperger and Sheather in the American
Statistician (May 1992 Vol 46 p79) in which they give an example of an
lms regression where one small data entry error made a huge difference
in the fit (on data for which a linear model is not unreasponable).
(My thanks to colleague John Grove for showing me this paper.)
The phenomenon behind this real world example is precisely the same as
in my toy example, but it would be immune to much of the criticism the
latter received.

The moral is that robust methods should be taken as just one more set of
exploratory tools, part of a broader analysis. However, I've seen lots of
examples where people have blindly dropped data into a robust procedure,
and talken the result without further analysis (under the assumption
that all they've lost is some power). This is likely to become more
common, especially in areas of engineering and finance where there is
motivation to have computers build quite complex models in real time
with little or no human intervention. Heck, I'm often tempted to do
something similar myself.

- David R.