{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30644",
  "author_total": 4,
  "authors": [
    {
      "name": "Jiaye Chen"
    },
    {
      "name": "Rui Qiu"
    },
    {
      "name": "Roulin Wang"
    },
    {
      "name": "Zhou Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ce2rprbyp5zad.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30644",
  "fulltext_url": null,
  "id": "ce2rprbyp5zad",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30644",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7204915275",
  "pdf_url": "https://arxiv.org/pdf/2608.30644",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ce2rprbyp5zad.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:54Z",
      "native_id": "2608.30644",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30644"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Marginal Coordinate Test for Fréchet Regression with Random Objects",
  "title_text": "Marginal Coordinate Test for Fréchet Regression with Random Objects",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:54Z",
  "url": "https://research.draconitic.com/paper/ce2rprbyp5zad",
  "venue": "arXiv",
  "versions": []
}