  Covariance matrices are important tools for obtaining reliable parameter
constraints. Advancements in cosmological surveys lead to larger data vectors
and, consequently, increasingly complex covariance matrices, whose number of
elements grows as the square of the size of the data vector. The most
straightforward way of comparing these matrices, in terms of their ability to
produce parameter constraints, involves a full cosmological analysis, which can
be very computationally expensive. Using the concept and construction of
compression schemes, which have become increasingly popular, we propose a fast
and reliable way of comparing covariance matrices. The basic idea is to focus
only on the portion of the covariance matrix that is relevant for the parameter
constraints and quantify, via a fast Monte Carlo simulation, the difference of
a second candidate matrix from the baseline one. To test this method, we apply
it to two covariance matrices that were used to analyse the cosmic shear
measurements for the Dark Energy Survey Year 1. We found that the uncertainties
on the parameters change by 2.6%, a figure in agreement with the full
cosmological analysis. While our approximate method cannot replace a full
analysis, it may be useful during the development and validation of codes that
estimate covariance matrices. Our method takes roughly 100 times less CPUh than
a full cosmological analysis.
