Gaussian Approximation and Spatially Dependent Wild Bootstrap for High-Dimensional Spatial Data

Daisuke Kurisu, Kengo Kato, Xiaofeng Shao

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we establish a high-dimensional CLT for the sample mean of p-dimensional spatial data observed over irregularly spaced sampling sites in (Formula presented.), allowing the dimension p to be much larger than the sample size n. We adopt a stochastic sampling scheme that can generate irregularly spaced sampling sites in a flexible manner and include both pure increasing domain and mixed increasing domain frameworks. To facilitate statistical inference, we develop the spatially dependent wild bootstrap (SDWB) and justify its asymptotic validity in high dimensions by deriving error bounds that hold almost surely conditionally on the stochastic sampling sites. Our dependence conditions on the underlying random field cover a wide class of random fields such as Gaussian random fields and continuous autoregressive moving average random fields. Through numerical simulations and a real data analysis, we demonstrate the usefulness of our bootstrap-based inference in several applications, including joint confidence interval construction for high-dimensional spatial data and change-point detection for spatio-temporal data. Supplementary materials for this article are available online.

Original languageEnglish (US)
JournalJournal of the American Statistical Association
DOIs
StateAccepted/In press - 2023

Keywords

  • Change-point analysis
  • High-dimensional central limit theorem
  • Irregularly spaced spatial data
  • Spatio-temporal data

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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