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Bias and variance of angular correlation functions
Abstract
We present a general method for calculating the bias and variance of estimators for w(θ) based on galaxy-galaxy (DD), random-random (RR), and galaxy-random (DR) pair counts and describe a procedure for quickly estimating these quantities given an arbitrary two-point correlation function and sampling geometry. These results, based conditionally upon the number counts, are accurate for both high and low number counts. We show explicit analytical results for the variances in the estimators DD/RR, DD/DR, which turn out to be considerably larger than the common wisdom Poisson estimate and report a small bias in DD/DR in addition to that due to the integral constraint. Further, we introduce and recommend an improved estimator (DD - 2DR + RR)/RR, whose variance is nearly Poisson.
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Cited by
Beutler, F., Blake, C., Colless, M., Jones, D. H., Staveley-Smith, L., Campbell, L., Parker, Q., Saunders, W., & Watson, F. (2011) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2011.19250.x · Cited by 2,590
“The redshift correlation function itself is given by Landy & Szalay (1993): ξ′data(s) = 1 + DD(s) RR(s) ( nr nd )2 − 2DR(s) RR(s) ( nr nd ) , (4) where the ratio nr/nd is given by nr nd = ∑Nr i wi(~x) ∑Nd j wj(~x) (5) and the sums go over all random (Nr) and data (Nd) galaxies.”
MethodLarge-scale structure of the Universe and cosmological perturbation theory
Bernardeau, F., Colombi, S., Gaztañaga, E., & Scoccimarro, R. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00135-7 · Cited by 1,922
The clustering of the SDSS DR7 main Galaxy sample – I. A 4 per cent distance measure at z=0.15
Ross, A. J., Samushia, L., Howlett, C., Percival, W. J., Burden, A., & Manera, M. (2015) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stv154 · Cited by 1,745
“…the correlation function as a function of the redshiftspace separation s and the Cosine of the angle to the line-of-sight, µ, using the standard Landy & Szalay (1993) method ξ(s, µ) = DD(s, µ)− 2DR(s, µ) +RR(s, µ) RR(s, µ) , (3) where D represents the galaxy sample and R represents the…”
MethodUniverseMachine: The correlation between galaxy growth and dark matter halo assembly from z = 0−10
Behroozi, P., Wechsler, R. H., Hearin, A. P., & Conroy, C. (2019) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stz1182 · Cited by 1,243
KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing
Hildebrandt, H., Viola, M., Heymans, C., Joudaki, S., Kuijken, K., Blake, C., Erben, T., Joachimi, B., Klaes, D., Miller, L., et al. (2017) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stw2805 · Cited by 1,021
Metadata
- Authors
- Landy, S. D., & Szalay, A. S.
- Venue
- The Astrophysical Journal
- Publisher
- American Astronomical Society
- Published
- 1993-07
- Volume
- 412
- Pages
- 64
- ISSN
- 0004-637X (ISSN-L)
- 1538-4357
- OpenAlex
- W2025634246
- Cited by
- 1,953
- References
- 0
- FWCI
- 3.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- Landy, S. D., & Szalay, A. S. (1993). Bias and variance of angular correlation functions. The Astrophysical Journal. https://doi.org/10.1086/172900
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