2000
DOI: 10.1086/312702
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A Comparison of Estimators for the Two-Point Correlation Function

Abstract: Nine of the most important estimators known for the two-point correlation function are compared using a predetermined, rigorous criterion. The indicators were extracted from over 500 subsamples of the Virgo Hubble volume simulation cluster catalog. The "real" correlation function was determined from the full survey in a 3000 h(-1) Mpc periodic cube. The estimators were ranked by the cumulative probability of returning a value within a certain tolerance of the real correlation function. This criterion takes int… Show more

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Cited by 216 publications
(233 citation statements)
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References 27 publications
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“…As was the case for the 3D real-space correlation ξ shown in Fig. 13, and in agreement with previous works (Kerscher et al 2000), the covariance is much smaller and more diagonal for the Landy & Szalay estimator (85) than for the Peebles & Hauser estimator (78). This can also be clearly seen from the comparison of the left and middle panels of Fig.…”
Section: Comparison Of Peebles and Hauser And Landy And Szalay Covariancesupporting
confidence: 92%
See 1 more Smart Citation
“…As was the case for the 3D real-space correlation ξ shown in Fig. 13, and in agreement with previous works (Kerscher et al 2000), the covariance is much smaller and more diagonal for the Landy & Szalay estimator (85) than for the Peebles & Hauser estimator (78). This can also be clearly seen from the comparison of the left and middle panels of Fig.…”
Section: Comparison Of Peebles and Hauser And Landy And Szalay Covariancesupporting
confidence: 92%
“…In agreement with Eqs. (67) and (69) and with standard results (Kerscher et al 2000), the covariance of the Landy & Szalay estimator (55) is smaller than for the Peebles & Hauser estimator (47), especially for the lower mass threshold (the higher mass threshold case being more dominated by the common shot-noise contribution (64)).…”
Section: Comparison Of Peebles and Hauser And Landy And Szalay Covariancesupporting
confidence: 57%
“…This fact, however, does not mean that its variance will be any more controllable for a wider class of distributions with more complex correlation properties than Poisson's (Gabrielli et al 2005). Indeed, there is no formal proof that the DP is less accurate than the LS for a generally correlated point distribution even though this conclusion has been reached by, e.g., Kerscher et al (2000) examining some specific properties of estimators in Nbody simulations. They concluded also that the H estimator is equivalent to the LS one.…”
Section: Pairwise Estimatorsmentioning
confidence: 99%
“…The effect of bias, i.e. finite volume or size effects, can be studied through the analysis of artificial simulations with known properties; however the three estimators defined above are all biased (Kerscher 1999;Kerscher et al 2000;Sylos Labini & Vasilyev 2008). It is worth noticing that Kerscher (1999) showed that, in a real galaxy sample, the three different estimators defined above use different finite size corrections yielding to different results on large enough scales, for small value of the correlation amplitude, while all of them agree on smaller scales, where the amplitude of the correlation was large enough.…”
Section: Pairwise Estimatorsmentioning
confidence: 99%
“…The properties of the angular correlation function and the estimators used to measure it from photometric catalogs have been extensively discussed in the astronomical literature (Kerscher, Szapudi, & Szalay 2000). The probability of finding a galaxy within a solid angle on the celestial plane of the sky at distance h from a randomly chosen object is given by (Peebles 1980, p. 174)…”
Section: The Angular Correlation Functionmentioning
confidence: 99%