BIAS AND VARIANCE OF ANGULAR-CORRELATION FUNCTIONS

We present a general method for calculating the bias and variance of e stimators for w(theta) based on galaxy-galaxy (DD), random-random (RR) , and galaxy-random (DR) pair counts and describe a procedure for quic kly estimating these quantities given an arbitrary two-point correlati on function and sampling geometry. These results, based conditionally upon the number counts, are accurate for both high and low number coun ts. We show explicit analytical results for the variances in the estim ators 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 add ition to that due to the integral constraint. Further, we introduce an d recommend an improved estimator (DD - 2DR + RR)/RR, whose variance i s nearly Poisson.