  The Projection Congruent Subset (PCS) Outlyingness is a new index of
multivariate outlyingness obtained by considering univariate projections of the
data. Like many other outlier detection procedures, PCS searches for a subset
which minimizes a criterion. The difference is that the new criterion was
designed to be insensitive to the outliers. PCS is supported by FastPCS, a fast
and affine equivariant algorithm which we also detail. Both an extensive
simulation study and a real data application from the field of engineering show
that FastPCS performs better than its competitors.
