The Effect of Covariance Estimator Error on Cosmological Parameter Constraints

Extracting parameter constraints from cosmological observations requires accurate determination of the covariance matrix for use in the likelihood function. We show here that uncertainties in the elements of the covariance matrix propagate directly to increased uncertainties in cosmological parameters. When the covariance matrix is determined by simulations, the resulting variance of the each parameter increases by a factor of order $1+N_b/N_s$ where $N_b$ is the number of bands in the measurement and $N_s$ is the number of simulations.