Marginal Coordinate Test for Fréchet Regression with Random Objects
Abstract
We develop a marginal coordinate test for regression with Euclidean predictors and a random-object response in a separable metric space. The goal is to test whether a predictor provides additional information about the response conditional on the remaining predictors. In a semi-supervised design, an unlabeled sample is used to estimate predictor conditional means, while an independent labeled sample is reserved for inference. The resulting residuals are combined with a product-space kernel to form a kernel conditional mean dependence (KCMD) U-statistic without requiring a response residual. The primary identity-based test targets a necessary conditional mean restriction, while a multiple-transformation extension probes broader alternatives. We establish a weighted centered chi-square null limit, wild bootstrap validity, consistency against fixed detectable alternatives, and local power under mean-element alternatives. For simultaneous inference, truncated p-to-e calibration combined with e-BH provides asymptotic false discovery rate control under general dependence. Simulations with Euclidean and non-Euclidean responses, together with a New York City taxi-flow analysis, illustrate the method.
Related
- Robust Local Fréchet Regression: Nonasymptotic Theory and Minimax Optimality
- Semi-Supervised Kernel Ridge Fréchet Regression
- Unrestricted conditional maximum likelihood estimation for a Fréchet regression model
- Phylogenetic Inference and the Stickiness of Fréchet Means, via Precise Asymptotics of an Embedded Random Walk
- Association and independence test for random objects
BibTeX
@misc{chen2026marginal,
title = {{Marginal Coordinate Test for Fréchet Regression with Random Objects}},
author = {Jiaye Chen and Rui Qiu and Roulin Wang and Zhou Yu},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30644},
eprint = {2608.30644},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30644},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Marginal Coordinate Test for Fréchet Regression with Random Objects
AU - Jiaye Chen
AU - Rui Qiu
AU - Roulin Wang
AU - Zhou Yu
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30644
UR - https://arxiv.org/abs/2608.30644
AB - We develop a marginal coordinate test for regression with Euclidean predictors and a random-object response in a separable metric space. The goal is to test whether a predictor provides additional information about the response conditional on the remaining predictors. In a semi-supervised design, an unlabeled sample is used to estimate predictor conditional means, while an independent labeled sample is reserved for inference. The resulting residuals are combined with a product-space kernel to form a kernel conditional mean dependence (KCMD) U-statistic without requiring a response residual. The primary identity-based test targets a necessary conditional mean restriction, while a multiple-transformation extension probes broader alternatives. We establish a weighted centered chi-square null limit, wild bootstrap validity, consistency against fixed detectable alternatives, and local power under mean-element alternatives. For simultaneous inference, truncated p-to-e calibration combined with e-BH provides asymptotic false discovery rate control under general dependence. Simulations with Euclidean and non-Euclidean responses, together with a New York City taxi-flow analysis, illustrate the method.
ER -