# A Normality Test for High-dimensional Data based on a Nearest Neighbor Approach

arXiv: https://arxiv.org/abs/1904.05289 · HTML: https://mlsanity.com/paper/1904.05289/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2019.

## Built on by (most cited first, 3 of 3)

- [Two-Way Is Better Than One: Bidirectional Alignment with Cycle Consistency for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2606.05675/) (2026)
- [Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithm](https://mlsanity.com/paper/2310.08798/) (2023)
- [Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows](https://mlsanity.com/paper/2603.11756/) (2026)

## Abstract (arXiv)

Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when the dimension is larger than the number of observations. In this work, we propose a novel nonparametric test that utilizes the nearest neighbor information. The proposed method guarantees the asymptotic type I error control under the high-dimensional setting. Simulation studies verify the empirical size performance of the proposed test when the dimension grows with the sample size and at the same time exhibit a superior power performance of the new test compared with alternative methods. We also illustrate our approach through two popularly used data sets in high-dimensional classification and clustering literatures where deviation from the normality assumption may lead to invalid conclusions.