Spatial Subsample Bootstraps for High-dimensional Spatial Data with Irregular Spacing

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 dependence 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.