Bias and variance of angular correlation functions

Details Bias and variance of angular correlation functions Bias and variance of angular correlation functions

Jul 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...412...64l&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 412, no. 1, p. 64-71.

Statistics

Computation

577

Angular Correlation, Bias, Computational Astrophysics, Galactic Clusters, Variance, Correlation Coefficients, Monte Carlo Method, Random Variables

Scientific paper

We present a general method for calculating the bias and variance of estimators for w(theta) 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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