Comparing Estimators of the Galaxy Correlation Function

We present a systematic comparison of some of the usual estimators of the two-point correlation function, some of them currently used in cosmology, others extensively employed in the field of the statistical analysis of point processes. At small scales it is known that the correlation function follows reasonably well a power-law expression ξ(r) ∝ r-γ. The accurate determination of the exponent γ (the order of the pole) depends on the estimator used for ξ(r); on the other hand, its behavior at large scales gives information on a possible trend to homogeneity. We study the concept, the possible bias, the dependence on random samples, and the errors of each estimator. Errors are computed by means of artificial catalogs of Cox processes for which the analytical expression of the correlation function is known. We also introduce a new method for extracting simulated galaxy samples from cosmological simulations.

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