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

• 成果类型: Article
• 署名作者: Kurisu, Daisuke; Kato, Kengo; Shao, Xiaofeng
• 署名单位: University of Tokyo; Cornell University; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2218578
• 发表日期: 2024
• 页码: 1820-1832
• 关键词: central limit-theorem; Empirical Processes; U-statistics; maxima; CONVERGENCE; variance; suprema; models; sums

摘要

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 Rd, 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. for this article are available online.