{
  "abstract": "The classical Whittle formula provides a closedform expression for the asymptotic Fisher information matrix (FIM) rate of multidimensional, real-valued, zero-mean, purely nondeterministic stationary Gaussian processes (GPs), expressed in terms of their parameterized spectra within a maximumlikelihood framework. However, the Gaussian assumption underlying this result restricts its applicability to many realworld signals exhibiting heavy-tailed or non-Gaussian behavior. In this paper, we extend Whittle's result to multidimensional, real-valued stationary compound Gaussian processes (CGPs) with arbitrary mean, under a unified framework encompassing fully known, parameterized, and completely unknown density generators. Building upon the Slepian-Bangs formula for n consecutive observations and extending it to the semiparametric setting, we leverage the asymptotic properties of block Toeplitz matrices to obtain a closed-form spectral-domain expression for the asymptotic FIM rate. The resulting expression, common to all density generator families, generalizes the standard zero-mean Gaussian formula by incorporating a distribution-dependent contribution associated with the nonzero mean, and an additional covariance term that is invariant to the choice of non-Gaussian distribution. This extension enables efficient and theoretically grounded performance analysis for heavy-tailed signal processing applications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20469",
  "author_total": 3,
  "authors": [
    {
      "name": "Jean-Pierre Delmas"
    },
    {
      "name": "Habti Abeida"
    },
    {
      "name": "Stefano Fortunati"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5vyt6r1a4y0pw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20469",
  "fulltext_url": null,
  "id": "5vyt6r1a4y0pw",
  "issns": [],
  "landing_url": "https://hal.science/hal-05753545v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "hal",
      "0.stat"
    ],
    [
      "openalex",
      "2202|Radar Systems and Signal Processing"
    ]
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  "openalex": "W7213596438",
  "pdf_url": "https://hal.science/hal-05753545/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5vyt6r1a4y0pw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:36Z",
      "native_id": "hal-05753545",
      "source": "hal",
      "url": "https://hal.science/hal-05753545v1"
    },
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20469"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "On the parametric and semiparametric Fisher information matrix for non-zero mean stationary spherical invariant random processes",
  "title_text": "On the parametric and semiparametric Fisher information matrix for non-zero mean stationary spherical invariant random processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:29Z",
  "url": "https://research.draconitic.com/paper/5vyt6r1a4y0pw",
  "venue": "HAL",
  "versions": []
}