{
  "abstract": "For linear regression with i.i.d. homoskedastic errors, optimally weighted second-order least squares (SLS) is the degree-two polynomial maximization method (PMM) estimating equation: both select the same optimal combination of $e$ and $e^2-σ^2$, share one influence function, and attain the slope variance $c_2g_2/N$. The identity is one of estimating equations and stops where the optimal combination depends on the design. Within the polynomial moment class, degree three holds an efficiency reserve: on four right-skewed laws the cubic direction adds between $30\\%$ and $50\\%$ asymptotic efficiency, and under symmetric platykurtic errors it is the only informative direction. The reserve belongs to the degree-three span, which an efficient generalized method of moments estimator also attains. We give the asymptotic law of the feasible plug-in estimator, a rule for choosing the degree, Lean 4 checks of the algebra, and simulation evidence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.11421",
  "author_total": 1,
  "authors": [
    {
      "name": "Serhii Zabolotnii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89vctmvbqzsgy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.11421",
  "fulltext_url": null,
  "id": "89vctmvbqzsgy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.11421",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Advanced Statistical Methods and Models"
    ]
  ],
  "openalex": "W7164394782",
  "pdf_url": "https://arxiv.org/pdf/2606.11421",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89vctmvbqzsgy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2606.11421",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.11421"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Second-Order Least Squares as a Special Case of the Polynomial Maximization Method",
  "title_text": "Second-Order Least Squares as a Special Case of the Polynomial Maximization Method",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/89vctmvbqzsgy",
  "venue": "arXiv",
  "versions": []
}