OWA operators in linear regression and detection of outliers

We consider the use of Ordered Weighted Averaging (OWA) in linear regression. Our goal is to replace the traditional least squares, least absolute deviation, and maximum likelihood criteria with an OWA function of the residuals. We obtain several high breakdown robust regression methods as special cases (least median, least trimmed squares, trimmed likelihood methods). We also present new formulations of regression problem. OWA-based regression is particularly useful in the presence of outliers.<br />