  Recent measurements of the centrality and rapidity dependence of single
inclusive jet production in p+Pb collisions at the LHC have revealed large and
non-trivial nuclear modification of the production cross section for this
process. In this paper, we explore to what extent such nuclear modification can
be understood by the framework of standard cold nuclear matter effects, in
particular initial-state cold nuclear matter energy loss. We demonstrate
quantitatively that theoretical calculations which include medium-induced
radiative corrections can describe rather reasonably the attenuation of the jet
production yields in the large transverse momentum region in d+Au collisions at
RHIC and p+Pb collisions at the LHC for central to semi-central collisions. We
further show that the observed scaling behavior of the nuclear modification
factor as a function of the total jet energy $p_T\, {\cosh} (y)$ for various
rapidity intervals has a natural explanation in the picture of cold nuclear
matter energy loss. On the other hand, the observed enhancement in peripheral
collisions is not described in this picture and could have a different origin.
