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

arXiv: https://arxiv.org/abs/1612.06601 · HTML: https://mlsanity.com/paper/1612.06601/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2016.

## Built on by (most cited first, 1 of 1)

- [Scenario generation for market risk models using generative neural networks](https://mlsanity.com/paper/2109.10072/) (2021)

## Abstract (arXiv)

We present a unified approach to goodness-of-fit testing in ℝd and on lower-dimensional manifolds embedded in ℝd 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 α-entropy between probability distributions. A simulation study shows that the procedures are serious competitors to established goodness-of-fit tests.