  Constraining cosmological parameters from measurements of the Integrated
Sachs-Wolfe effect requires developing robust and accurate methods for
computing statistical errors in the cross-correlation between maps. This paper
presents a detailed comparison of such error estimation applied to the case of
cross-correlation of Cosmic Microwave Background (CMB) and large-scale
structure data. We compare theoretical models for error estimation with
montecarlo simulations where both the galaxy and the CMB maps vary around a
fiducial auto-correlation and cross-correlation model which agrees well with
the current concordance LCDM cosmology. Our analysis compares estimators both
in harmonic and configuration (or real) space, quantifies the accuracy of the
error analysis and discuss the impact of partial sky survey area and the choice
of input fiducial model on dark-energy constraints. We show that purely
analytic approaches yield accurate errors even in surveys that cover only 10%
of the sky and that parameter constraints strongly depend on the fiducial model
employed. Alternatively, we discuss the advantages and limitations of error
estimators that can be directly applied to data. In particular, we show that
errors and covariances from the Jack-Knife method agree well with the
theoretical approaches and simulations. We also introduce a novel method in
real space that is computationally efficient and can be applied to real data
and realistic survey geometries. Finally, we present a number of new findings
and prescriptions that can be useful for analysis of real data and forecasts,
and present a critical summary of the analyses done to date.
