Least Median Squares is often argued to give more stable results than does OLS. Whereas in OLS one minimises the mean of squared residuals, in LMS, one instead minimises the median of squared residuals. Intuitively, should give estimators that are largely (completely?) invariant to outliers. As such, i would have thought this approach would find a natural home in finance applications, however, I haven't come across it being used (a search on this site, for example gives zero citations).
Does any one recommend or discourage a LMS approach - say, for a simple case of estimating a beta coefficient between two securities?