A robust nonparametric test for spatial isotropy in lattice data

2026-05-18

AI Summary

This study addresses the failure of conventional isotropy tests in lattice spatial data due to isolated or clustered outliers. To overcome this limitation, a robust nonparametric testing procedure is proposed, integrating a divergence-based robust variogram estimator with a block permutation resampling scheme. The method effectively controls Type I error rates under strong spatial dependence and contamination by outliers, thereby enhancing both stability and reliability of isotropy assessment. Empirical evaluation demonstrates its practical utility in analyzing Landsat 8 satellite imagery affected by cloud cover, where it successfully identifies isotropic structures despite significant data interference.

Abstract

This paper proposes a robust test for assessing isotropy based on the variogram of spatial data on a two-dimensional regular grid. The test is based on the non-robust subsampling test for isotropy of Guan et al. (2004), which uses the idea of comparing variogram estimates in diff erent directions at the same distance. The robust test employs robust variogram esti- mators which are based on estimators of univariate or multivariate scatter and perform well in the presence of isolated or block outliers. Additionally, a diff erent resampling method, called block permutation, is proposed. Compared with the subsampling test, the block per- mutation test maintains the signifi cance level even for strong dependencies in the data and is robust to outliers. The methods are illustrated by an application to Landsat 8 satellite data, where outlier blocks may occur due to, for example, clouds.

Problem

• spatial isotropy
• robust test
• variogram
• outliers
• lattice data

Innovation

• robust variogram
• spatial isotropy
• block permutation
• nonparametric test
• outlier robustness