  We present a study on the robustness of the covariance matrix estimation for
galaxy clustering measurements depending on the cosmological parameters and
galaxy bias. To this end, we have produced 9000 galaxy mock catalogues relying
on the effective Zel'dovich approximation implemented in the EZmocks computer
code, using different input cosmological models and bias parameters. The
reference catalogue has also been produced with this code making our study
insensitive to the approximation at least on a relative-qualitative level. Our
findings indicate that the covariance matrix is insensitive to the input power
spectrum (including $\sigma_8$), as long as the 2- and 3-point galaxy
clustering measurements agree with the given data. In fact, the covariance
matrix shows a bias at small scales ($r\lesssim40 h^{-1}$Mpc) when the chosen
galaxy bias parameters yield a 3-point statistics, which is not compatible with
the reference one within the error bars, even though the 2-point statistics
agree within 1%. Nevertheless, the error becomes negligible at large scales
making the covariance matrix still reliable for data analysis using only
measurements in that regime (e.g., measuring baryon acoustic oscillations).
  High precision in cosmological parameter estimation is expected for
covariance matrices extracted from mock galaxy catalogues which take accurately
into account both the 2- and the 3- point statistics. This is independent of
whether this is achieved by using the right cosmology and galaxy bias (which
are not a priori known) or just any combination of both fitting the net
observed galaxy clustering.
