Ordinal patterns based testing of spatial independence in irregular spatial structures.

Area of Science:

• Spatial statistics
• Nonparametric methods
• Data analysis

Background:

• Traditional spatial independence tests often assume regular data lattices.
• Irregularly distributed spatial data are common in many scientific fields.
• Existing methods may lack robustness to outliers or transformations.

Purpose of the Study:

• To propose a novel nonparametric test for spatial independence.
• To extend ordinal pattern analysis to irregular spatial point clouds.
• To provide a robust and asymptotically pivotal statistical procedure.

Main Methods:

• Encoding local spatial configurations using ordinal patterns of nearest neighbors.
• Symbolic representation invariant to monotone transformations and robust to outliers.
• Constructing a test statistic based on empirical ordinal pattern frequencies and log-ratio transformation.
• Applying a central limit theorem for graph-dependent processes under α-mixing conditions.

Main Results:

• The test statistic converges to a chi-squared distribution (χm!-12), providing an asymptotically pivotal test.
• Monte Carlo simulations confirm accurate approximation and control of Type I error rate.
• The test demonstrates power to detect spatial dependence in various models, including nonlinear ones.
• The method effectively handles irregularly located data points.

Conclusions:

• The proposed ordinal pattern test is a powerful and robust tool for assessing spatial independence on irregular supports.
• This framework expands the applicability of ordinal pattern methods to a wider range of real-world spatial data.
• The test offers a valuable addition to the toolkit for spatial data analysis in diverse scientific disciplines.