An inverse problem approach to robust regression

When recording data, large errors may occur occasionally. The corresponding abnormal data points, called outliers, can have drastic effects on the estimates. There are several ways to cope with outliers-detect and delete or adjust the erroneous data,-use a modified cost function. We propose a new approach that allows, by introducing additional variables, to model the outliers and to detect their presence. In the standard linear regression model this leads to a linear inverse problem that, associated with a criterion that ensures sparseness, is solved by a quadratic programming algorithm. The new approach (model+criterion) allows for extensions that cannot be handled by the usual robust regression methods.