A robust nonparametric test for spatial isotropy in lattice data

TL;DR

This paper introduces a robust, block permutation-based nonparametric test for spatial isotropy in lattice data, effective even with outliers and strong dependencies, demonstrated on satellite imagery.

Contribution

It develops a new robust isotropy test using variogram estimators and block permutation resampling, improving robustness over existing methods.

Findings

The test maintains significance levels under strong dependencies.

It is robust to outliers such as clouds in satellite data.

Application to Landsat 8 data illustrates practical effectiveness.

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.