Prediction of Spatial Cumulative Distribution Functions Using Subsampling
提出一种空间子抽样方法，基于六边形网格观测数据预测空间累积分布函数，并证明该方法能准确近似预测器的抽样分布，用于估计分位数和加权均方积分误差等总体特征。
Abstract The spatial cumulative distribution function (SCDF) is a random function that provides a statistical summary of a random field over a spatial domain of interest. In this article we develop a spatial subsampling method for predicting an SCDF based on observations made on a hexagonal grid, similar to the one used in the Environmental Monitoring and Assessment Program of the U.S. Environmental Protection Agency. We show that under quite general conditions, the proposed subsampling method provides accurate data-based approximations to the sampling distributions of various functionals of the SCDF predictor. In particular, it produces estimators of different population characteristics, such as the quantiles and weighted mean integrated squared errors of the empirical predictor. As an illustration, we apply the subsampling method to construct large-sample prediction bands for the SCDF of an ecological index for foliage condition of red maple trees in the state of Maine.