{
  "abstract": "The polynomial maximization method estimates signal parameters in non-Gaussian noise from a finite description of the noise by its moments and cumulants, without a density. Known accuracy results assume that these noise characteristics are known, or use a design in which estimating them jointly costs no accuracy. In practice they are estimated from the residuals of a preliminary fit, and the effect of this substitution on accuracy is unknown. We treat the feasible scheme as a two-step estimator and, for a general smooth signal model in a fixed design, find the increment of its asymptotic covariance in closed form: $Σ_{\\rm fe}-Σ_{\\rm or}=c_2(1-g_{\\rm or}) Q^{-1}\\bar{d}\\bar{d}^{\\top}Q^{-1}$, a positive semidefinite matrix of rank at most one. Here $c_2$ is the noise variance, $g_{\\rm or}\\le 1$ the oracle variance reduction factor, and $Q$ and $\\bar{d}$ the second-moment matrix and mean of the signal gradient over the design. Estimating the fractional moments that form the weights costs no first-order accuracy, because that block is orthogonal; the whole increment comes from estimating the sign-preserving centering means. The increment lies along the single direction $Q^{-1}\\bar{d}$, so linear combinations of the parameters orthogonal to it keep oracle accuracy. In the trace metric the variance reduction factor becomes $g_{\\rm fe}=g_{\\rm or}+(1-g_{\\rm or})R_D$, where $R_D=\\|Q^{-1}\\bar{d}\\|^2/{\\rm tr} Q^{-1}$ depends on the design alone. We give four sufficient conditions for first-order oracle equivalence; noise symmetry is not among them. Monte Carlo experiments with a harmonic signal confirm the direction and size of the increment. A covariance estimate that ignores the increment undercovers where non-Gaussianity gives the largest gain, symmetric noise included.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05511",
  "author_total": 1,
  "authors": [
    {
      "name": "Serhii Zabolotnii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/exw2caxs3by4n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05511",
  "fulltext_url": null,
  "id": "exw2caxs3by4n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05511",
  "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",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2604|Statistical and numerical algorithms"
    ]
  ],
  "openalex": "W7220726390",
  "pdf_url": "https://arxiv.org/pdf/2610.05511",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/exw2caxs3by4n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.05511",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05511"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Rank-one variance inflation in polynomial estimation of signal parameters with a sign-preserving fractional-power basis",
  "title_text": "Rank-one variance inflation in polynomial estimation of signal parameters with a sign-preserving fractional-power basis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/exw2caxs3by4n",
  "venue": "arXiv",
  "versions": []
}