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

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  • Max Sommerfeld
  • Stephan Sain
  • Armin Schwartzman

Abstract

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.

Suggested Citation

  • Max Sommerfeld & Stephan Sain & Armin Schwartzman, 2018. "Confidence Regions for Spatial Excursion Sets From Repeated Random Field Observations, With an Application to Climate," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1327-1340, July.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:523:p:1327-1340
    DOI: 10.1080/01621459.2017.1341838
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    Cited by:

    1. Karine Hagesæther Foss & Gunhild Elisabeth Berget & Jo Eidsvik, 2022. "Using an autonomous underwater vehicle with onboard stochastic advection‐diffusion models to map excursion sets of environmental variables," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
    2. Soham Sarkar & Victor M. Panaretos, 2022. "CovNet: Covariance networks for functional data on multidimensional domains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1785-1820, November.
    3. Zhang, Likun & Castillo, Enrique del & Berglund, Andrew J. & Tingley, Martin P. & Govind, Nirmal, 2020. "Computing confidence intervals from massive data via penalized quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    4. Telschow, Fabian J.E. & Davenport, Samuel & Schwartzman, Armin, 2022. "Functional delta residuals and applications to simultaneous confidence bands of moment based statistics," Journal of Multivariate Analysis, Elsevier, vol. 192(C).

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