Multivariate goodness-of-fit on flat and curved spaces via nearest neighbor distances

Bruno Ebner; Norbert Henze; Joseph E. Yukich

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arXiv · 1612.06601

Multivariate goodness-of-fit on flat and curved spaces via nearest neighbor distances

Bruno Ebner·Norbert Henze·Joseph E. Yukich

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Abstract

We present a unified approach to goodness-of-fit testing in $\mathbb{R}^d$ and on lower-dimensional manifolds embedded in $\mathbb{R}^d$ based on sums of powers of weighted volumes of $k$-th nearest neighbor spheres. We prove asymptotic normality of a class of test statistics under the null hypothesis and under fixed alternatives. Under such alternatives, scaled versions of the test statistics converge to the $\alpha$-entropy between probability distributions. A simulation study shows that the procedures are serious competitors to established goodness-of-fit tests.

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Bruno Ebner, Norbert Henze, Joseph E. Yukich. 2016-12-20. Multivariate goodness-of-fit on flat and curved spaces via nearest neighbor distances. https://arxiv.org/abs/1612.06601

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