  We use analytic covariance matrices to carry out a full-shape analysis of the
galaxy power spectrum multipoles from the Baryon Oscillation Spectroscopic
Survey (BOSS). We obtain parameter estimates that agree well with those based
on the sample covariance from two thousand galaxy mock catalogs, thus
validating the analytic approach and providing substantial reduction in
computational cost. We also highlight a number of additional advantages of
analytic covariances. First, the analysis does not suffer from sampling noise,
which biases the constraints and typically requires inflating parameter error
bars. Second, it allows us to study convergence of the cosmological constraints
when recomputing the analytic covariances to match the best-fit power spectrum,
which can be done at a negligible computational cost, unlike when using mock
catalogs. These effects reduce the systematic error budget of cosmological
constraints, which suggests that the analytic approach may be an important tool
for upcoming high-precision galaxy redshift surveys such as DESI and Euclid.
Finally, we study the impact of various ingredients in the power spectrum
covariance matrix and show that the non-Gaussian part, which includes the
regular trispectrum and super-sample covariance, has a marginal effect
($\lesssim 10 \%$) on the cosmological parameter error bars. We also suggest
improvements to analytic covariances that are commonly used in Fisher
forecasts.
