Validating spatial-temporal separability for stationary processes

TL;DR

This paper develops nonparametric statistical methods to validate the separability assumption in spatial-temporal covariance structures without relying on spectral methods or normality, applicable under various asymptotics.

Contribution

It introduces a novel, nonparametric inference framework for testing spatial-temporal separability that does not assume normality or spectral decomposition, with asymptotic distribution results.

Findings

Derived asymptotic distributions for deviation measures

Developed confidence intervals and hypothesis tests for separability

Applicable under both domain-expanding-infill and domain-expanding asymptotics

Abstract

A crucial assumption to reduce computational complexity in spatial-temporal data analysis is separability, which factors the covariance structure into a purely spatial and a purely temporal component. In this paper, we develop statistical inference tools for validating this assumption for a second-order stationary process under both domain-expanding-infill asymptotics and domain-expanding asymptotics. In contrast to previous work on this subject, the methodology neither requires the assumption of normally distributed data, nor uses spectral methods. Our approach is based on nonparametric estimates of measures for the deviation between the covariance matrix and separable approximations, which vanish if and only if the assumption of separability is satisfied. We derive the asymptotic distributions of appropriate estimators for these measures with non-standard limiting distributions and use these results to develop inference tools for validating the assumption of separability. More specifically, we derive confidence intervals for the deviation measures, tests for the hypothesis of exact separability, and for the hypothesis that the deviation from separability is smaller than a prespecified threshold.