Data analysis from upcoming large galaxy redshift surveys, such as Euclid and
DESI will significantly improve constraints on cosmological parameters. To
optimally extract the information from these galaxy surveys, it is important to
control with a high level of confidence the uncertainty and bias arising from
the estimation of the covariance that affects the inference of cosmological
parameters. In this work, we are addressing two different but closely related
issues: (i) the sampling noise present in a covariance matrix estimated from a
finite set of simulations and (ii) the impact on cosmological constraints of
the non-Gaussian contribution to the covariance matrix of the power spectrum.
We focus on the parameter estimation obtained from fitting the matter power
spectrum in real space, using the DEMNUni N-body simulations. Regarding the
first issue, we adopt two different approaches to reduce the sampling noise in
the precision matrix that propagates in the parameter space: on the one hand
using an alternative estimator of the covariance matrix based on a non-linear
shrinkage, NERCOME; and on the other hand employing a method of fast generation
of approximate mock catalogs, COVMOS. We find that NERCOME can significantly
reduce the noise induced on the posterior distribution of parameters, but at
the cost of a systematic overestimation of the error bars on the cosmological
parameters. We show that using a COVMOS covariance matrix estimated from a
large number of realisations (10~000) results in unbiased cosmological
constraints. Regarding the second issue, we quantify the impact on cosmological
constraints of the non-Gaussian part of the power spectrum covariance purely
coming from non-linear clustering. We find that when this term is neglected,
both the errors and central values of the estimated parameters are affected for
a scale cut \kmax > 0.2\ \invMpc.Comment: 21 pages, 2 appendices, 20 figures. Submitted to A&