Robust Nonparametric Testing Approaches for Spatial Regression

TL;DR

This paper introduces a robust nonparametric Monte Carlo testing framework for spatial regression that effectively assesses covariate significance without relying on restrictive parametric assumptions.

Contribution

It develops a novel random shift-based testing approach that maintains validity under model misspecification and does not require a closed-form distribution of test statistics.

Findings

The method maintains the nominal significance level in simulations.

It achieves competitive power compared to parametric methods.

Parametric methods can have inflated type I error under misspecification.

Abstract

Reliable inference for spatial regression remains challenging because it requires the correct specification of the spatial dependence structure, the mean trend, and the error distribution. Existing parametric testing methods rely on restrictive assumptions that are difficult to verify in practice and can lead to inaccurate conclusions under misspecification. To address this, we develop a robust nonparametric Monte Carlo testing framework for spatial regression based on random shifts. We construct test statistics that measure the dependence between residuals, obtained after removing the effects of nuisance covariates, and the covariate of interest. This allows us to assess the significance of the covariate in the sense of partial correlation. The proposed framework enables robust inference across various models without requiring parametric assumptions or even a closed-form distribution of the test statistics. Furthermore, we establish the asymptotic exactness of the random shift test in the increasing-domain setting when the sample covariance is used as the test statistic. Through extensive numerical experiments, we demonstrate that our method maintains the nominal significance level while achieving competitive power, whereas parametric methods can exhibit inflated type I error rates, even when they are correctly specified.