Testing multivariate uniformity based on random geometric graphs
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We present new families of goodness-of-fit tests of uniformity on a full-dimensional set W⊂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.
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