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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

Abstract

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.

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Bruno Ebner. Franz Nestmann. Matthias Schulte. "Testing multivariate uniformity based on random geometric graphs." Electron. J. Statist. 14 (2) 4273 - 4320, 2020. https://doi.org/10.1214/20-EJS1776

Information

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

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

Subjects:
Primary: 62G10
Secondary: 62G20, 60D05

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Vol.14 • No. 2 • 2020
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