Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images

TL;DR

This paper introduces a new class of goodness-of-fit tests for complete spatial randomness that leverage Minkowski functionals of binary images, providing an efficient and competitive alternative to existing methods.

Contribution

The paper develops a novel testing procedure based on geometric functionals of transformed binary images, with proven asymptotic properties and practical applicability.

Findings

Tests are computationally efficient.

Simulations show strong performance compared to existing tests.

Applied successfully to gamma-ray astronomy data.

Abstract

We propose a class of goodness-of-fit tests for complete spatial randomness (CSR). In contrast to standard tests, our procedure utilizes a transformation of the data to a binary image, which is then characterized by geometric functionals. Under a suitable limiting regime, we derive the asymptotic distribution of the test statistics under the null hypothesis and almost sure limits under certain alternatives. The new tests are computationally efficient, and simulations show that they are strong competitors to other tests of CSR. The tests are applied to a real data set in gamma-ray astronomy, and immediate extensions are presented to encourage further work.