Abstract

We develop a class of spatial subsample bootstrap (SSB) methods for high-dimensional

spatial data observed at irregular locations. The proposed procedures approximate the distributions

of high-dimensional spatial statistics under general spatial dependence without requiring regular

sampling designs or explicit estimation of dependence structures. Two implementations are studied:

the spatial multiplier subsample bootstrap (SMSB) and the spatial empirical subsample bootstrap

(SESB), both constructed from overlapping spatial subsample statistics. We establish asymptotic

validity of the proposed methods for joint distributional approximation of high-dimensional statistics, including max-type and studentized statistics, under mild moment and weak spatial depen-

dence conditions. The dimension of the parameter is allowed to diverge with the sample size and

may exceed it. The proposed framework avoids estimation of high-dimensional covariance matrices

and remains computationally efficient in high-dimensional regimes. We further derive an asymptotically optimal subsample size by balancing the leading bias and variance terms of the bootstrap

approximation and propose a data-driven plug-in selector with optimality guarantees. The results

provide a general theoretical foundation for bootstrap-based inference in high-dimensional spatial

problems with irregular designs.

Key words and phrases: Bootstrap, Gaussian approximation, high-dimensional statistical inference, irregularly spaced spatial data resampling methods spatial statistics 1

Information

Preprint No.SS-2026-0032
Manuscript IDSS-2026-0032
Complete AuthorsYue Li, Shibin Zhang
Corresponding AuthorsShibin Zhang
Emailszhang_shibin@shnu.edu.cn

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Acknowledgments

The authors thank the associate editor and anonymous reviewers for their helpful comments. This work was supported in part by the Natural Science Foundation of Shanghai

(grant number: 23ZR1447100).

Supplementary Materials

The online Supplementary Material contains additional simulation results and proofs of

the main results.

Supplementary materials are available for download.