Consistent specification testing under spatial dependence

TL;DR

This paper introduces a new series-based nonparametric test for regression functions that accounts for complex spatial dependence, with theoretical validation and practical applications demonstrated through simulations and real data.

Contribution

It develops a novel specification test that handles various forms of spatial dependence, including high-dimensional and semiparametric cases, with proven asymptotic normality.

Findings

Test statistic is asymptotically standard normal under new dependence conditions.

Bootstrap method effectively improves finite sample performance.

Empirical examples demonstrate practical applicability.

Abstract

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing dimension, semiparametric or any combination thereof, thus covering a vast variety of settings. These include spatial error models of varying types and levels of complexity. Under a new smooth spatial dependence condition, our test statistic is asymptotically standard normal. To prove the latter property, we establish a central limit theorem for quadratic forms in linear processes in an increasing dimension setting. Finite sample performance is investigated in a simulation study, with a bootstrap method also justified and illustrated, and empirical examples illustrate the test with real-world data.