# Direction-Projection-Permutation for High Dimensional Hypothesis Tests

arXiv: https://arxiv.org/abs/1304.0796 · HTML: https://mlsanity.com/paper/1304.0796/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2013.

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

- [Integral Probability Metrics Meet Neural Networks: The Radon-Kolmogorov-Smirnov Test](https://mlsanity.com/paper/2309.02422/) (2023)
- [Measure of Strength of Evidence for Visually Observed Differences between Subpopulations](https://mlsanity.com/paper/2101.00362/) (2021)
- [Non-Euclidean Analysis of Joint Variations in Multi-Object Shapes](https://mlsanity.com/paper/2109.02230/) (2021)

## Abstract (arXiv)

Motivated by the prevalence of high dimensional low sample size datasets in modern statistical applications, we propose a general nonparametric framework, Direction-Projection-Permutation (DiProPerm), for testing high dimensional hypotheses. The method is aimed at rigorous testing of whether lower dimensional visual differences are statistically significant. Theoretical analysis under the non-classical asymptotic regime of dimension going to infinity for fixed sample size reveals that certain natural variations of DiProPerm can have very different behaviors. An empirical power study both confirms the theoretical results and suggests DiProPerm is a powerful test in many settings. Finally DiProPerm is applied to a high dimensional gene expression dataset.