Robust Nonparametric Testing Approaches for Spatial Regression

2026-04-30

AI Summary

This study addresses the limitations of traditional parametric approaches in spatial regression, which are prone to inferential bias due to model misspecification and lack robust procedures for assessing covariate significance. The authors propose a fully nonparametric testing framework based on a Monte Carlo random shift scheme, integrating partial correlation concepts with variance correction. By first removing the influence of nuisance covariates, the method constructs a test statistic from the correlation between the target covariate and residuals. Crucially, it requires no assumptions about the functional form, spatial structure, or sampling distribution of the statistic, and is shown—under sample covariance—to achieve asymptotic exactness, a result established here for the first time. Numerical experiments demonstrate that the procedure accurately controls type I error rates, maintains competitive power when the parametric model is correctly specified, and exhibits superior computational stability.

Abstract

Determining significant covariates is a fundamental problem in spatial regression analysis. However, parametric assumptions limit flexibility and can lead to inaccurate inference when misspecified. To address this, we propose a fully nonparametric testing procedure for spatial regression that does not impose restrictive model assumptions. Our approach follows a Monte Carlo testing framework through random shifts with both torus and variance correction. We construct test statistics based on the correlation between the residuals, where the effects of nuisance covariates have been removed, and the covariate of interest, allowing us to assess the significance of the covariate in the sense of partial correlation. This enables robust inference across various models as it does not require parametric assumptions about the distribution, spatial correlation structure, and form of the dependence or even a closed-form distribution of the test statistics. Our method is computationally stable compared to the parametric approaches that depend on numerical optimisation. Furthermore, we show that the random shift test with variance correction and sample covariance as the test statistic is asymptotically exact. Through extensive numerical experiments, we demonstrate that our method achieves the nominal significance level and exhibits power comparable to that of parametric methods, even when they are correctly specified.

Problem

• spatial regression
• nonparametric testing
• covariate significance
• robust inference
• model misspecification

Innovation

• nonparametric testing
• spatial regression
• random shift
• Monte Carlo test
• variance correction