Performance of internal covariance estimators for cosmic shear correlation functions

• Published in: Monthly notices of the Royal Astronomical Society 2016-03, Vol.456 (3), p.2662-2680
• Main Authors: Friedrich, O., Seitz, S., Eifler, T. F., Gruen, D.
• Format: Article
• Language: English
• Subjects: Constants; Convergence; Cosmology; Covariance; Dark energy; Estimating; Galaxies; Shear; Simulation; Star & galaxy formation; Statistics; Symbols; Uncertainty
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stv2833

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 ${\sim } 5000 \deg ^2$ 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 ≳85 per cent of the volume derived from the true covariance matrix. The uncertainty on the parameter combination $\Sigma _8 \sim \sigma _8 \Omega _{\rm m}^{0.5}$ derived from internally estimated covariances is ∼90 per cent of the true uncertainty.