A test for directional-linear independence, with applications to wildfire orientation and size

TL;DR

This paper introduces a nonparametric test for assessing independence between wildfire orientation and size, using a directional-linear kernel density estimator, with applications demonstrated on Portuguese wildfire data.

Contribution

The paper develops a novel nonparametric test for directional-linear independence and provides a practical resampling procedure, with performance evaluation and real-world wildfire data application.

Findings

The test effectively detects independence between wildfire orientation and size.

Simulation studies show competitive performance compared to classical tests.

Application to Portuguese wildfire data reveals significant dependence patterns.

Abstract

The relation between wildfire orientation and size is analyzed by means of a nonparametric test for directional-linear independence. The test statistic is designed for assessing the independence between two random variables of different nature, specifically directional (fire orientation, circular or spherical, as particular cases) and linear (fire size measured as burnt area, scalar), based on a directional-linear nonparametric kernel density estimator. In order to apply the proposed methodology in practice, a resampling procedure based on permutations and bootstrap is provided. The finite sample performance of the test is assessed by a simulation study, comparing its behavior with other classical tests for the circular-linear case. Finally, the test is applied to analyze wildfire data from Portugal.