Statistical Analysis of Galaxy Surveys-I. Robust error estimation for 2-point clustering statistics

We present a test of different error estimators for 2-point clustering statistics, appropriate for present and future large galaxy redshift surveys. Using an ensemble of very large dark matter ΛCDM N-body simulations, we compare internal error estimators (jackknife and bootstrap) to external ones (Monte-Carlo realizations). For 3-dimensional clustering statistics, we find that none of the internal error methods investigated are able to reproduce neither accurately nor robustly the errors of external estimators on 1 to 25 h Mpc scales. The standard bootstrap overestimates the variance of ξ(s) by ∼ 40% on all scales probed, but recovers, in a robust fashion, the principal eigenvectors of the underlying covariance matrix. The jackknife returns the correct variance on large scales, but significantly overestimates it on smaller scales. This scale dependence in the jackknife affects the recovered eigenvectors, which tend to disagree on small scales with the external estimates. Our results have important implications for the use of galaxy clustering in placing constraints on cosmological parameters. For example, in a 2-parameter fit to the projected correlation function, we find that the standard bootstrap systematically overestimates the 95 % confidence interval, while the jackknife method remains biased, but to a lesser extent. The scatter we find between realizations, for Gaussian statistics, implies that a 2-σ confidence interval, as inferred from an internal estimator, could correspond in practice to anything from 1-σ to 3-σ. Finally, by an oversampling of sub-volumes, it is possible to obtain bootstrap variances and confidence intervals that agree with external error estimates, but it is not clear if this prescription will work for a general case.