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Mathematics > Statistics Theory

arXiv:1812.08638 (math)
[Submitted on 20 Dec 2018 (v1), last revised 17 Jul 2020 (this version, v2)]

Title:Testing multivariate uniformity based on random geometric graphs

Authors:Bruno Ebner, Franz Nestmann, Matthias Schulte
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Abstract:We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ 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.
Comments: 36 pages, 2 figures
Subjects: Statistics Theory (math.ST); Probability (math.PR); Methodology (stat.ME)
MSC classes: Primary 62G10, Secondary 62G20, 60D05
Cite as: arXiv:1812.08638 [math.ST]
  (or arXiv:1812.08638v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.1812.08638

Submission history

From: Bruno Ebner [view email]
[v1] Thu, 20 Dec 2018 15:38:05 UTC (89 KB)
[v2] Fri, 17 Jul 2020 14:04:55 UTC (112 KB)
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