NONPARAMETRIC-ESTIMATION OF THE MOMENTS OF A GENERAL STATISTIC COMPUTED FROM SPATIAL DATA

A statistic s(-) is computed on spatially indexed data {X(i):i is-an-e lement-of D}, where D is a finite subset of the integer lattice Z2. We propose a simple nonparametric method for estimating the moments (e.g ., variance, skewness) of s(D), using only the observed data at hand. The method uses ''replicates'' of s(.) computed on smaller subsets of D. No explicit knowledge of the underlying spatial dependence mechanis m is needed, and the marginal distribution of X(i) may also be unknown . The shape of D can be quite irregular, and s(.) is allowed to be a g eneral statistic. The proposed estimator is shown to be consistent and asymptotically normal (under mild conditions on s(D) and ''mixing'' c onditions on the strength of spatial dependence). As a numerical examp le, the estimator is used in assessing the geographic clumping of canc er deaths in the United States.