  The anomalous Hall effect is deemed to be a unique transport property of
ferromagnetic metals, caused by the concerted action of spin polarization and
spin-orbit coupling. Nevertheless, recent experiments have shown that the
effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic
insulator (yttrium iron garnet (YIG)), even when precautions are taken to
ensure there is no induced magnetization in the metal. We propose a theory of
this effect based on the combined action of spin-dependent scattering from the
magnetic interface and the spin Hall effect in the bulk of the metal. At
variance with previous theories, we predict the effect to be of first order in
the spin-orbit coupling, just as the conventional anomalous Hall effect -- the
only difference being the spatial separation of the spin orbit interaction and
the magnetization. For this reason we name this effect \textit{nonlocal
anomalous Hall effect} and predict that its sign will be determined by the sign
of the spin Hall angle in the metal. The AH conductivity that we calculate from
our theory is in good agreement with the measured values in Pt/YIG structures.
