  In this paper, we obtain boundary Harnack estimates and comparison theorem
for nonnegative solutions to the linearized Monge-Amp\`ere equations under
natural assumptions on the domain, Monge-Amp\`ere measures and boundary data.
Our results are boundary versions of Caffarelli and Guti\'errez's interior
Harnack inequality for the linearized Monge-Amp\`ere equations. As an
application, we obtain sharp upper bound and global $L^p$-integrability for the
Green's function of the linearized Monge-Amp\`ere operator.
