  The Residual Congruent Subset (RCS) is a new method for finding outliers in
the linear regression setting. Like many other outlier detection procedures,
RCS searches for a subset which minimizes a criterion. The difference is that
the new criterion was designed to be insensitive to the outliers. RCS is
supported by FastRCS, a fast regression and affine equivariant algorithm which
we also detail. Both an extensive simulation study and two real data
applications show that FastRCS performs better than its competitors.
