Variance Estimation for Statistics Computed from Spatial Lattice Data
提出一种仅利用空间格点数据本身来估计任意复杂统计量方差的方法，适用于不规则区域，无需分布假设，并证明了估计量的一致性及收敛速度。
SUMMARY A statistic s() is computed on spatially indexed data {X i: i ∈ D), where D is a finite subset of the integer lattice Z2. We propose a method for estimating the variance (and other moments) of s() by using only the data. The set D may be irregularly shaped, the statistic s() may be arbitrarily complicated and no distributional assumptions (marginal or joint) are necessary. The method uses the statistic computed on overlapping 'subshapes' of D as replicates of s(). The estimator is simply the sample variance of the (standardized) replicates. We demonstrate L 2-consistency of the estimator (under mild conditions on s() and the strength of spatial dependence). A rate of convergence is also given, giving guidance into the appropriate choice of subshape size, and the estimator is illustrated in two data examples.