{
  "abstract": "Characterizing longitudinal changes in region-specific distribution of environmental exposures, such as total nitrate (TNO$_3$) concentrations, is critical for understanding localized ecological risks that are otherwise obscured by standard mean-level modeling. However, modeling longitudinal distributional outcomes across spatial regions presents significant methodological challenges. The random objects are spatio-temporally dependent, and mathematical constraints are inherent to distributional representations, such as, monotonicity of quantile functions. To address this, we propose a novel spatially-indexed longitudinal distributional outcome regression model. The distributional coefficients corresponding to the fixed effects of covariates are modeled using Bernstein basis polynomials, while spatio-temporal random effects are flexibly captured via tensor product expansions of splines. We develop a scalable Markov Chain Monte Carlo (MCMC) algorithm to explicitly account for spatial dependencies, and introduce a fast two-stage projected-posterior approach to preserve the monotonicity of the predicted subject-specific quantile functions. Extensive simulation studies demonstrate that the proposed framework achieves superior estimation accuracy and predictive performance compared to standard non-spatial distributional outcome regression. We apply our methodology to predict monthly, site-specific distributions of TNO$_3$ concentrations across the contiguous United States. Accounting for spatial correlation provides substantially lower uncertainty in the estimated distributional effects and improves predictive performance over the non-spatial alternative, offering a robust, interpretable tool for spatio-temporal environmental monitoring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15961",
  "author_total": 3,
  "authors": [
    {
      "name": "Rahul Ghosal"
    },
    {
      "name": "Suman Majumder"
    },
    {
      "name": "Indranil Sahoo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cad4r0gg1q4q5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15961",
  "fulltext_url": null,
  "id": "cad4r0gg1q4q5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15961",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2002|Spatial and Panel Data Analysis"
    ]
  ],
  "openalex": "W7213344351",
  "pdf_url": "https://arxiv.org/pdf/2609.15961",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cad4r0gg1q4q5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:36Z",
      "native_id": "2609.15961",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15961"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Spatially-Indexed Longitudinal Distributional Outcome Regression for Environmental Monitoring",
  "title_text": "Spatially-Indexed Longitudinal Distributional Outcome Regression for Environmental Monitoring",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/cad4r0gg1q4q5",
  "venue": "arXiv",
  "versions": []
}