Gaussian approximation and spatially dependent wild bootstrap for high-dimensional spatial data
Gaussian approximation and spatially dependent wild bootstrap for high-dimensional spatial data
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DOI：
10.1080/01621459.2023.2218578
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发表时间：
2021-03
影响因子：
3.7
通讯作者：
Daisuke Kurisu;Kengo Kato;Xiaofeng Shao
中科院分区：
文献类型：
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作者：
Daisuke Kurisu;Kengo Kato;Xiaofeng Shao
在本文中，我们建立了一个高维CLT的$p$维空间数据的样本平均值在$\mathbb{R}^d$上不规则间隔的采样点，允许维度$p$远远大于样本大小$n$。我们采用随机抽样方案，可以产生不规则间隔的采样点，在一个灵活的方式，包括纯增加域和混合增加域框架。为了便于统计推断，我们开发了空间依赖的野生自助（SDWB），并证明其在高维的渐近有效性，通过推导误差界，几乎肯定有条件的随机抽样网站。我们的依赖条件的基础上的随机场覆盖了广泛的一类随机场，如高斯随机场和连续自回归移动平均随机场。通过数值模拟和真实的数据分析，我们证明了基于Bootstrap的推理在多个应用中的有用性，包括高维空间数据的联合置信区间构建和时空数据的变点检测。
In this paper, we establish a high-dimensional CLT for the sample mean of $p$-dimensional spatial data observed over irregularly spaced sampling sites in $\mathbb{R}^d$, 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.