Abstract

In frequency domain analysis for spatial data, spectral averages based on the periodogram often play

an important role in understanding spatial covariance structure, but also have complicated sampling

distributions due to complex variances from aggregated periodograms. In order to non-parametrically

approximate these sampling distributions for purposes of inference, resampling can be useful, but previous developments in spatial bootstrap have faced challenges in the scope of their validity, specifically

due to issues in capturing the complex variances of spatial spectral averages. As a consequence, existing frequency domain bootstraps for spatial data are highly restricted in application to only special

processes (e.g. Gaussian) or certain spatial statistics. To address this limitation and to approximate a

wide range of spatial spectral averages, we propose a practical hybrid-resampling approach that combines two different resampling techniques in the forms of spatial subsampling and spatial bootstrap.

Subsampling helps to capture the variance of spectral averages while bootstrap captures the distributional shape. The hybrid resampling procedure can then accurately quantify uncertainty in spectral

inference under mild spatial assumptions. Moreover, compared to the more studied time series setting,

this work fills a gap in the theory of subsampling/bootstrap for spatial data regarding spectral average

statistics.

Key words and phrases: Spatial Frequency Domain Bootstrap, Spectral Mean, Periodogram

Information

Preprint No.SS-2025-0204
Manuscript IDSS-2025-0204
Complete AuthorsSouvick Bera, Daniel Nordman, Soutir Bandyopadhyay
Corresponding AuthorsSoutir Bandyopadhyay
Emailsbsoutir@gmail.com

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Acknowledgments

The authors are grateful to the Associate Editor, and the two reviewers for thoughtful

comments that substantially improved the manuscript. The authors are also thankful to

NSF for the NSF ACCESS MTH250064 allocation and for support by NSF DMS-2514857

(Bera and Bandyopadhyay) and 2515719 (Nordman).

Supplementary Materials

present additional finite sample simulation results in support of the

proposed method, along with proof details of technical lemmas. Figures and tables presented

in this paper are generated using code available in the GitHub repository: HFDB git.

Supplementary materials are available for download.