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<p>The stationarity assumption is often not appropriate for modeling spatial data over large spatial domains. While the observed spatial field may be amenable to modeling by stationary random fields over smaller parts of the domain, a framework is needed to allow for (smooth) variations, both of the scaling (or the variance function) and of the spatial interactions (i.e., the spatial dependence structure) across the entire spatial domain. In this paper, we provide a formulation of locally stationary random fields that allows for such variations in the spatial covariance function. We present fairly general constructions in both the frequency and spatial domains, deriving an estimator for the local covariance based on irregularly spaced samples from the spatial process. We also establish consistency of the local covariance estimator and obtain an expansion for its mean squared error (MSE). Results from a moderately large simulation study illustrate finite sample properties of the proposed estimator.</p>

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Locally Stationary Spatial Processes

  • 期刊论文

  • 发表日期：

    2025年7月25日

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  • Soumendra N. Lahiri,
  • Tucker McElroy,
  • Daniel Weinberg

摘要

The stationarity assumption is often not appropriate for modeling spatial data over large spatial domains. While the observed spatial field may be amenable to modeling by stationary random fields over smaller parts of the domain, a framework is needed to allow for (smooth) variations, both of the scaling (or the variance function) and of the spatial interactions (i.e., the spatial dependence structure) across the entire spatial domain. In this paper, we provide a formulation of locally stationary random fields that allows for such variations in the spatial covariance function. We present fairly general constructions in both the frequency and spatial domains, deriving an estimator for the local covariance based on irregularly spaced samples from the spatial process. We also establish consistency of the local covariance estimator and obtain an expansion for its mean squared error (MSE). Results from a moderately large simulation study illustrate finite sample properties of the proposed estimator.