# Fr'echet Covariance and MANOVA Tests for Random Objects in Multiple Metric Spaces

arXiv: https://arxiv.org/abs/2306.12066 · HTML: https://mlsanity.com/paper/2306.12066/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2023.

## Built on by (most cited first, 4 of 4)

- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [Variable Selection Methods for Multivariate, Functional, and Complex Biomedical Data in the AI Age](https://mlsanity.com/paper/2501.06868/) (2025)
- [Random-Effects Algorithm for Random Objects in Metric Spaces](https://mlsanity.com/paper/2605.02693/) (2026)

## Abstract (arXiv)

In this manuscript we consider random objects being measured in multiple metric spaces, which may arise when those objects may be measured in multiple distinct ways. In this new multivariate setting, we define a Fr'echet covariance and Fr'echet correlation in two metric spaces, and a Fr'echet covariance matrix and Fr'echet correlation matrix in an arbitrary number of metric spaces. We prove consistency for the sample Fr'echet covariance, and propose several tests to compare the means and covariance matrices between two or more groups. Lastly, we investigate the power and Type I error of each test under a variety of scenarios.