Open Access
Translator Disclaimer
2020 Testing multivariate uniformity based on random geometric graphs
Bruno Ebner, Franz Nestmann, Matthias Schulte
Electron. J. Statist. 14(2): 4273-4320 (2020). DOI: 10.1214/20-EJS1776


We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset \mathbb{R}^{d}$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the null hypothesis as well as under fixed alternatives. The derived tests are consistent and their behaviour for some contiguous alternatives can be controlled. A simulation study suggests that the procedures can compete with or are better than established goodness-of-fit tests. We show with a real data example that the new tests can detect non-uniformity of a small sample data set, where most of the competitors fail.


Download Citation

Bruno Ebner. Franz Nestmann. Matthias Schulte. "Testing multivariate uniformity based on random geometric graphs." Electron. J. Statist. 14 (2) 4273 - 4320, 2020.


Received: 1 July 2020; Published: 2020
First available in Project Euclid: 12 December 2020

MathSciNet: MR4187135
Digital Object Identifier: 10.1214/20-EJS1776

Primary: 62G10
Secondary: 62G20, 60D05

Keywords: $U$-statistics , contiguous alternatives , Gilbert graph , Multivariate goodness-of-fit test , Random geometric graph , uniform distribution


Vol.14 • No. 2 • 2020
Back to Top