  A class of improved estimators is proposed for N-point correlation functions
of galaxy clustering, and for discrete spatial random processes in general. In
the limit of weak clustering, the variance of the unbiased estimator converges
to the continuum value much faster than with any alternative, all terms giving
rise to a slower convergence exactly cancel. Explicit variance formulae are
provided for both Poisson and multinomial point processes using techniques for
spatial statistics reported by Ripley (1988). The formalism naturally includes
most previously used statistical tools such as N-point correlation functions
and their Fourier counterparts, moments of counts-in-cells, and moment
correlators. For all these, and perhaps some other statistics our estimator
provides a straightforward means for efficient edge corrections.
