{
  "abstract": "We provide sufficient conditions for the consistency of penalized least squares procedures that select the order (dimension) of a regression model from a sequence of nested classes, allowing for dependent, martingale-difference errors. The main contribution is to relax the classical identifiability requirement: parameters indexing classes larger than the true order need not be identified, provided the additional, excess directions admit a linear approximation to the truth in a neighbourhood of the true parameter. This relaxation lets the number of candidate models grow with the sample size, removing the usual need for a fixed upper bound. We verify the resulting high-level conditions for two classes of nonlinear regression models used in applied work: multiple-regime smooth transition regression and mixture-of-experts models with generic generalized linear model experts. Under a BIC-type penalty, the resulting order selection rule is consistent in either model class whenever the number of candidate models grows slower than the logarithm of the sample size.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23220",
  "author_total": 1,
  "authors": [
    {
      "name": "Eduardo Fonseca Mendes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d323yhbc0kypw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23220",
  "fulltext_url": null,
  "id": "d323yhbc0kypw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23220",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "econ.EM"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7213998027",
  "pdf_url": "https://arxiv.org/pdf/2609.23220",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d323yhbc0kypw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:33Z",
      "native_id": "2609.23220",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23220"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Consistent Order Selection under Non-Identifiability and Dependence",
  "title_text": "Consistent Order Selection under Non-Identifiability and Dependence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/d323yhbc0kypw",
  "venue": "arXiv",
  "versions": []
}