Moments of Ioffe time parton distribution functions from non-local matrix elements

We examine the relation of moments of parton distribution functions to matrix elements of non-local operators computed in lattice quantum chromodynamics. We argue that after the continuum limit is taken, these non-local matrix elements give access to moments that are finite and can be matched to those defined in the $\overline{MS}$ scheme. We demonstrate this fact with a numerical computation of moments through non-local matrix elements in the quenched approximation and we find that these moments are in excellent agreement with the moments obtained from direct computations of local twist-2 matrix elements in the quenched approximation.