Performance of internal covariance estimators for cosmic shear correlation functions

Abstract

Data re-sampling methods such as delete-one jackknife, bootstrap or the sub-sample covariance are common tools for estimating the covariance of large-scale structure probes. We investigate different implementations of these methods in the context of cosmic shear two-point statistics. Using lognormal simulations of the convergence field and the corresponding shear field we generate mock catalogues of a known and realistic covariance. For a survey of {Ëœ } 5000 ° ^2 we find that jackknife, if implemented by deleting sub-volumes of galaxies, provides the most reliable covariance estimates. Bootstrap, in the common implementation of drawing sub-volumes of galaxies, strongly overestimates the statistical uncertainties. In a forecast for the complete 5-yr Dark Energy 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 â‰_s1185 per cent of the volume derived from the true covariance matrix. The uncertainty on the parameter combination Σ _8 Ëœ σ _8 Ω _m^{0.5} derived from internally estimated covariances is Ëœ90 per cent of the true uncertainty.