On the inadequacy of internal covariance estimation for super-sample covariance [CEA]


We give an analytical understanding of how subsamples-based internal covariance estimators lead to biased estimates of the covariance due to underestimating the super-sample covariance (SSC). This includes jackknife and bootstrap as estimators for the full survey area, and subsampling as an estimator of the covariance of subsamples. The limitations of the jackknife covariance have been previously presented in the literature, basically because it is effectively a rescaling of the covariance of the subsample area. However we point out that subsampling is also biased but for a different reason: the subsamples are not independent, and the corresponding lack of power results in SSC underprediction. We develop the formalism in the case of cluster counts that allows to predict exactly the bias of each covariance estimator. We find significant effects for a small scale area or when a low number of subsamples is used, with auto-redshift biases ranging from 0.4% to 15% for subsampling and from 5% to 75% for jackknife covariance estimates. The cross-redshift covariance is even more affected, with biases ranging from 8% to 25% for subsampling and from 50% to 90% for jackknife. Due to the redshift evolution of the probe, the covariances cannot be debiased by a simple rescaling factor, and an exact debiasing has the same requirements as the full SSC prediction. These results thus disfavour the use of internal covariance estimators on data itself or a simulation, leaving analytical predictions and separate universe simulations as possible SSC predictors.

Read this paper on arXiv…

F. Lacasa and M. Kunz
Fri, 10 Mar 17

Comments: 7 pages, 6 figures