  We develop a procedure that transforms any asymptotically normal estimator
into an asymptotically normal estimator whose distribution is robust to
arbitrary data contamination. More generally, our procedure transforms any
estimator whose asymptotic distribution has positive and continuous density at
the origin into an asymptotically normal estimator whose distribution is robust
to arbitrary contamination. In developing such a procedure we prove new general
properties of componentwise and geometric quantiles in both finite and infinite
dimensions.
