Confidence Regions for Spatial Excursion Sets From Repeated Random Field Observations, With an Application to Climate
针对重复噪声观测下的空间函数，提出基于乘子自助法的置信区域构建方法，用于确定北美地区21世纪中期夏季和冬季平均气温升高超过2摄氏度的区域。
The goal of this paper is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations. Given an asymptotically Gaussian estimator of the target function, a pair of data-dependent nested excursion sets are constructed that are sub- and super-sets of the true excursion set, respectively, with a desired confidence. Asymptotic coverage probabilities are determined via a multiplier bootstrap method, not requiring Gaussianity of the original data nor stationarity or smoothness of the limiting Gaussian field. The method is used to determine regions in North America where the mean summer and winter temperatures are expected to increase by mid 21st century by more than 2 degrees Celsius.