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We introduce a new method to test spatial dependence in random fields using Hilbert curves to convert data into time series. This approach is flexible, robust, and extends beyond 3D, offering a practical alternative to existing methods.

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Area of Science:

  • Geostatistics
  • Spatial Statistics
  • Time Series Analysis

Background:

  • Testing spatial dependence is crucial in analyzing random fields.
  • Existing methods for spatial ordinal patterns are often limited to 2D.
  • A flexible and robust nonparametric framework is needed.

Purpose of the Study:

  • To propose a novel nonparametric framework for testing spatial dependence in random fields.
  • To extend spatial dependence testing beyond two and three dimensions.
  • To offer a practical and general alternative to current methods.

Main Methods:

  • Spatial data is converted into one-dimensional time series using space-filling Hilbert curves.
  • Ordinal pattern-based tests for serial dependence are applied to the transformed sequence.
  • Generalized Hilbert (gilbert) curves are used to accommodate arbitrary grid sizes.

Main Results:

  • Spatial dependence in random fields is effectively transformed into serial dependence.
  • The proposed framework demonstrates flexibility and robustness.
  • The method naturally extends to dimensions beyond three.

Conclusions:

  • The Hilbert curve transformation provides a powerful tool for analyzing spatial dependence.
  • This nonparametric framework offers a versatile and scalable solution for geostatistical analysis.
  • The approach overcomes limitations of existing methods, enabling broader applications.