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Testing multivariate uniformity based on random geometric graphs

Ebner, Bruno; Nestmann, Franz; Schulte, Matthias

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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Verlagsausgabe §
DOI: 10.5445/IR/1000129568
Veröffentlicht am 11.02.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 1935-7524
KITopen-ID: 1000129568
Erschienen in Electronic journal of statistics
Verlag Institute of Mathematical Statistics (IMS)
Band 14
Heft 2
Seiten 4273-4320
Nachgewiesen in Scopus
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