Isotropy testing in spatial point patterns: nonparametric versus parametric replication under misspecification

TL;DR

This paper compares parametric and nonparametric methods for testing isotropy in spatial point patterns, highlighting the robustness of nonparametric approaches under model misspecification through extensive simulations.

Contribution

It introduces a general framework for integrating nonparametric replication methods into isotropy testing and evaluates their performance against parametric methods under misspecification.

Findings

Nonparametric methods maintain test size and power better under model misspecification.

Parametric methods are sensitive to model misspecification, leading to distorted test results.

Nonparametric replication offers a robust alternative for isotropy testing in practical scenarios.

Abstract

Several hypothesis testing methods have been proposed to validate the assumption of isotropy in spatial point patterns. A majority of these methods are characterised by an unknown distribution of the test statistic under the null hypothesis of isotropy. Parametric approaches to approximating the distribution involve simulation of patterns from a user-specified isotropic model. Alternatively, nonparametric replicates of the test statistic under isotropy can be used to waive the need for specifying a model. In this paper, we first present a general framework which allows for the integration of a selected nonparametric replication method into isotropy testing. We then conduct a large simulation study comprising application-like scenarios to assess the performance of tests with different parametric and nonparametric replication methods. In particular, we explore distortions in test size and power caused by model misspecification, and demonstrate the advantages of nonparametric replication in such scenarios.