Heavy tailed spatial autocorrelation models

TL;DR

This paper introduces the tSAR model, extending traditional SAR models to heavy-tailed error distributions using the t-distribution, improving modeling of spatial autocorrelation in data with heavy tails.

Contribution

The paper proposes the tSAR model, an extension of SAR models with t-distributed errors, and provides variance estimation considering spatial structure, validated through simulations and a fire danger application.

Findings

tSAR model performs well in simulations

tSAR improves fit over SAR in heavy-tailed data

Application to fire danger shows notable improvement

Abstract

Appropriate models for spatially autocorrelated data account for the fact that observations are not independent. A popular model in this context is the simultaneous autoregressive (SAR) model that allows to model the spatial dependency structure of a response variable and the influence of covariates on this variable. This spatial regression model assumes that the error follows a normal distribution. Since this assumption cannot always be met, it is necessary to extend this model to other error distributions. We propose the extension to the $t$-distribution, the tSAR model, which can be used if we observe heavy tails in the fitted residuals of the SAR model. In addition, we provide a variance estimate that considers the spatial structure of a variable which helps us to specify inputs for our models. An extended simulation study shows that the proposed estimators of the tSAR model are performing well and in an application to fire danger we see that the tSAR model is a notable improvement compared to the SAR model.