I Szapudi | PubMed Health

PubMed2001

Cosmic statistics of statistics: N-point correlations.

The fully general calculation of the cosmic error on N-point correlation functions and related quantities is presented. More precisely, the variance caused by the finite volume, discreteness, and edge effects is determined for any estimator which is based on a general function of N-tuples, such as multi-point correlation functions and multi-spectra. The results are printed explicitly for the two-point correlation function (or power-spectrum), and for the three-point correlation (or bispectrum). These are the most popular statistics in the study of large-scale structure, yet the general calculation of their variance has not been performed until now.

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PubMed2000

A Comparison of Estimators for the Two-Point Correlation Function.

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 into account bias and variance, and it is independent of the possibly non-Gaussian nature of the error statistics. As a result, for astrophysical applications, a clear recommendation has emerged: the Landy & Szalay estimator, in its original or grid version (Szapudi & Szalay), is preferred in comparison with the other indicators examined, with a performance almost indistinguishable from the Hamilton estimator.

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