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

Haoshu Xu; Hongzhe Li

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arXiv · 2506.23487

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

Haoshu Xu·Hongzhe Li

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Abstract

We propose a novel test for assessing partial effects in Fréchet 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.

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Haoshu Xu, Hongzhe Li. 2026-08-28. Test of partial effects for Frechet regression on Bures-Wasserstein manifolds. https://arxiv.org/abs/2506.23487

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