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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.10482 |
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Table of Contents:
- Modern regression analysis often involves responses and predictors taking values in the same or distinct metric spaces. To rank non-Euclidean heterogeneous predictors in regression by explanatory strength, analogous to the classical $R^2$, we introduce the Fréchet correlation coefficient (FCC), defined as the relative reduction in the Fréchet variance of the response after conditioning on a specific predictor. FCC is directional, model-free, and interpretable on a unit-scale, attaining one under almost sure functional dependence and zero when the Fréchet mean is invariant to conditioning. We propose a novel partition-based estimator that avoids explicit nonparametric estimation of the conditional Fréchet mean function, thereby improving both computational efficiency and flexibility. A tailored wild bootstrap algorithm is further developed for testing the Fréchet conditional mean dependence. We establish asymptotic theory and evaluate power through extensive simulations.