Confidence Regions for Spatial Excursion Sets From Repeated Random Field Observations, With an Application to Climate

• 成果类型: Article
• 署名作者: Sommerfeld, Max; Sain, Stephan; Schwartzman, Armin
• 署名单位: University of Gottingen; University of California System; University of California San Diego
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1341838
• 发表日期: 2018
• 页码: 1327-1340
• 关键词: nonparametric-estimation; Asymptotic Normality; Wild Bootstrap; LEVEL; estimators; prediction; signals

摘要

The goal of this article 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.