  In the present paper we contribute to the thermodynamic formalism of
partially hyperbolic attractors for local diffeomorphisms admitting an
invariant stable bundle and a positively invariant cone field with non-uniform
cone expansion at a positive Lebesgue measure set of points. These include the
case of attractors for Axiom A endomorphisms and partially hyperbolic
endomorphisms derived from Anosov. We prove these attractors have finitely many
SRB measures, that these are hyperbolic, and that the SRB measure is unique
provided the dynamics is transitive. Moreover, we show that the SRB measures
are statistically stable (in the weak$^*$ topology) and that their entropy
varies continuously with respect to the local diffeomorphism.
