Performance of internal Covariance Estimators for Cosmic Shear Correlation Functions

Data re-sampling methods such as the delete-one jackknife are a common tool for estimating the covariance of large scale structure probes. In this paper we investigate the concepts of internal covariance estimation in the context of cosmic shear two-point statistics. We demonstrate how to use log-normal simulations of the convergence field and the corresponding shear field to carry out realistic tests of internal covariance estimators and find that most estimators such as jackknife or sub-sample covariance can reach a satisfactory compromise between bias and variance of the estimated covariance. In a forecast for the complete, 5-year DES survey we show that internally estimated covariance matrices can provide a large fraction of the true uncertainties on cosmological parameters in a 2D cosmic shear analysis. The volume inside contours of constant likelihood in the Ωm-σ8 plane as measured with internally estimated covariance matrices is on average & 85% of the volume derived from the true covariance matrix. The uncertainty on the parameter combination Σ8 ∼ σ8Ω 0.5 m derived from internally estimated covariances is ∼ 90% of the true uncertainty.