Estimating the power spectrum covariance matrix with fewer mock samples
  The covariance matrices of power-spectrum (P(k)) measurements from galaxy
surveys are difficult to compute theoretically. The current best practice is to
estimate covariance matrices by computing a sample covariance of a large number
of mock catalogues. The next generation of galaxy surveys will require
thousands of large volume mocks to determine the covariance matrices to desired
accuracy. The errors in the inverse covariance matrix are larger and scale with
the number of P(k) bins, making the problem even more acute. We develop a
method of estimating covariance matrices using a theoretically justified,
few-parameter model, calibrated with mock catalogues. Using a set of 600 BOSS
DR11 mock catalogues, we show that a seven parameter model is sufficient to fit
the covariance matrix of BOSS DR11 P(k) measurements. The covariance computed
with this method is better than the sample covariance at any number of mocks
and only ~100 mocks are required for it to fully converge and the inverse
covariance matrix converges at the same rate. This method should work equally
well for the next generation of galaxy surveys, although a demand for higher
accuracy may require adding extra parameters to the fitting function.
