Creating jackknife and bootstrap estimates of the covariance matrix for the two-point correlation function

FG Mohammad, WJ Percival - Monthly Notices of the Royal …, 2022 - academic.oup.com
FG Mohammad, WJ Percival
Monthly Notices of the Royal Astronomical Society, 2022academic.oup.com
We present correction terms that allow delete-one Jackknife and Bootstrap methods to be
used to recover unbiased estimates of the data covariance matrix of the two-point correlation
function. We demonstrate the accuracy and precision of this new method using a large set of
1000 QUIJOTE simulations that each cover a comoving volume of. The corrected resampling
techniques recover the correct amplitude and structure of the data covariance matrix as
represented by its principal components to within∼ 10 per cent, the level of error achievable …
Abstract
We present correction terms that allow delete-one Jackknife and Bootstrap methods to be used to recover unbiased estimates of the data covariance matrix of the two-point correlation function . We demonstrate the accuracy and precision of this new method using a large set of 1000 QUIJOTE simulations that each cover a comoving volume of . The corrected resampling techniques recover the correct amplitude and structure of the data covariance matrix as represented by its principal components to within ∼10 per cent, the level of error achievable with the size of the sample of simulations used for the test. Our corrections for the internal resampling methods are shown to be robust against the intrinsic clustering of the cosmological tracers both in real- and redshift space using two snapshots at z = 0 and z = 1 that mimic two samples with significantly different clustering. We also analyse two different slicing of the simulation volume into or 125 sub-samples and show that the main impact of different is on the structure of the covariance matrix due to the limited number of independent internal realizations that can be made given a fixed .
Oxford University Press