  In this paper we provide a statistical analysis of the parameter-free method
often used in weak lensing mass reconstructions. It is found that a proper
assessment of the errors involved in such a non-local analysis requires the
study of the relevant two-point correlation functions. After calculating the
two-point correlation function for the reduced shear, we determine the expected
error on the inferred mass distribution and on other related quantities, such
as the total mass, and derive the error power spectrum. This allows us to
optimize the reconstruction method, with respect to the kernel used in the
inversion procedure. In particular, we find that curl-free kernels are bound to
lead to more accurate mass reconstructions. Our analytical results clarify the
arguments and the numerical simulations by Seitz & Schneider (1996).
