# Generalized Multivariate Signs for Nonparametric Hypothesis Testing in High Dimensions

arXiv: https://arxiv.org/abs/2107.01103 · HTML: https://mlsanity.com/paper/2107.01103/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 26 references that are in the map.
- First posted on arXiv 2 Jul 2021.

## Builds on (most cited first, 1 of 1)

- [Intrinsic Sliced Wasserstein Distances for Comparing Collections of Probability Distributions on Manifolds and Graphs](https://mlsanity.com/paper/2010.15285/) (2020)

## Abstract (arXiv)

High-dimensional data, where the dimension of the feature space is much larger than sample size, arise in a number of statistical applications. In this context, we construct the generalized multivariate sign transformation, defined as a vector divided by its norm. For different choices of the norm function, the resulting transformed vector adapts to certain geometrical features of the data distribution. Building up on this idea, we obtain one-sample and two-sample testing procedures for mean vectors of high-dimensional data using these generalized sign vectors. These tests are based on U-statistics using kernel inner products, do not require prohibitive assumptions, and are amenable to a fast randomization-based implementation. Through experiments in a number of data settings, we show that tests using generalized signs display higher power than existing tests, while maintaining nominal type-I error rates. Finally, we provide example applications on the MNIST and Minnesota Twin Studies genomic data.