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 ∼5000deg^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 Ω_m–σ_8 plane as measured with internally estimated covariance matrices is on average ≳85 per cent of the volume derived from the true covariance matrix. The uncertainty on the parameter combination Σ_8∼σ_8Ω^(0.5)_m derived from internally estimated covariances is ∼90 per cent of the true uncertainty.

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