Re: Summary of Robust Regression Algorithms

David Ross (
Mon, 5 Jan 98 19:02:33 HST

> Doug Martin sent me an e-mail suggesting that he may post to s-news some
> comments about the merit or lack of merit of robust procedures like
> least trimmed squares. I think that could spark a fun and lively
> debate. Go for it, Doug.

Packages (like S+), coupled with the ubiquity of remarkable computing
power, sometimes make it a bit *too* tempting to drop data into robust
procedures. I'm guilty of this myself (especially since the robustness
of lmsreg is backed up by a beautiful geometric characterization). In
anticipation of Doug Martin's response, let me offer (to anyone reading
this thread) an example I sometimes give my students. Suppose your
dataset has 2k+1 elements in it, k+1 of them take the value 0, and k of
them take the value 100. The median is therefore 0. Now, change one of
the 0s into a 100. The median is now 100. This is robust?

A similar example can be concocted for almost every procedure I
know with a high breakdown point (including lmsreg).

- David R. (