The errors ei in (1.1) are assumed to be independent and identically distributed, but are not necessarily normal and may be heavy-tailed. Assume for convenience that β is one dimensional. Then (1.1) is a simple linear regression. However, most of the following extends more-or-less easily to higher-dimensional β, in which case (1.1) is a multiple regression. Given β, define Ri(β) as the rank (or...

Ordinary Least Squares (OLS) is omnipresent in regression modeling. Occasionally Least Absolute Deviations (LAD) or other methods are used as an alternative when there are outliers. Although some data adaptive estimators have been proposed they are typically difficult to implement. In this note, we propose an easy to compute adaptive estimator which is simply a linear combination of OLS and LAD...