{
  "abstract": "Threshold and change-plane models provide a useful framework for capturing regime-dependent dynamics, but most existing approaches typically rely on scalar thresholds or linear splitting boundaries. We propose a scalable semiparametric change-plane regression framework that allows the regime boundary to depend nonlinearly on multivariate state variables. Random Fourier features provide a flexible and computationally efficient approximation to the nonlinear boundary function. A two-stage procedure first estimates the induced regime classification using a smooth surrogate and then refits the structural parameters by hard-threshold OLS. We establish convergence of the first-stage regime classification and show that its estimation error is asymptotically negligible for the second-stage refit, yielding oracle equivalence. We further develop a dependent-multiplier bootstrap Sup-Wald test for detecting the existence of regime effects when the boundary is unidentified under the null, and establish its asymptotic validity. Simulations demonstrate accurate regime recovery, near-oracle performance of the proposed estimator, and satisfactory finite-sample behavior of the Sup-Wald test. An application to postwar U.S. unemployment data provides strong evidence of regime dependence, while the estimated nonlinear change plane identifies a distinct stress regime characterized by significant shifts in short-run unemployment dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13290",
  "author_total": 2,
  "authors": [
    {
      "name": "Wei Liu"
    },
    {
      "name": "Shaogao Lv"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ewqm6g19dpa08.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13290",
  "fulltext_url": null,
  "id": "ewqm6g19dpa08",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13290",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7221549293",
  "pdf_url": "https://arxiv.org/pdf/2610.13290",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ewqm6g19dpa08.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:46Z",
      "native_id": "2610.13290",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13290"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Scalable Nonparametric Change-Plane Regression with Random Features: Estimation and Inference",
  "title_text": "Scalable Nonparametric Change-Plane Regression with Random Features: Estimation and Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:46Z",
  "url": "https://research.draconitic.com/paper/ewqm6g19dpa08",
  "venue": "arXiv",
  "versions": []
}