# Test of partial effects for Frechet regression on Bures-Wasserstein manifolds

arXiv: https://arxiv.org/abs/2506.23487 · HTML: https://mlsanity.com/paper/2506.23487/

## Key facts

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- First posted on arXiv 30 Jun 2025.

## Abstract (arXiv)

We propose a novel test for assessing partial effects in Fr'echet regression with responses lying on the Bures-Wasserstein manifold. Under the null hypothesis, we show that the statistic admits a degenerate V-statistic approximation whose limiting distribution is a weighted mixture of chi-squared random variables, with weights determined by the eigenvalues of an integral operator associated with a reproducing kernel Hilbert space (RKHS) kernel. We establish the asymptotic validity and consistency of the proposed test. Its finite-sample performance is examined through simulation studies. We apply the proposed test to study the effect of age, while controlling for other covariates, on gene co-expression structure in single-cell data.