{
  "abstract": "In this paper, we study the estimation of the signal subspace dimension $k$ in a $p$-variate signal-plus-noise complex Gaussian model, when the noise covariance matrix is assumed to be diagonal or Toeplitz. We consider the high-dimensional asymptotic regime in which both the data dimension $p$ and the available sample size $n$ diverge to infinity at the same rate, while we also allow $k$ to diverge at a slower speed. In this context, the classical estimates of the literature, consistent in the high-dimensional regime, often rely on the a priori knowledge of an upper bound $k_*$ of $k$, which can be misspecified in practice. Our proposed approach relies on building estimates of the tracial moments of the noise covariance matrix using the $p-k_*$ smallest eigenvalues of the sample covariance matrix (SCM), which are in turn used to build a threshold above which the $k$ largest eigenvalues are isolated. The resulting estimate of $k$ is proved to be consistent in the high-dimensional regime, even for the misspecified situations where $k_* < k$. Numerical experiments in different challenging scenarios illustrate the improvement of the proposed approach over the aforementioned methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18059",
  "author_total": 5,
  "authors": [
    {
      "name": "Hugo Jeannin"
    },
    {
      "name": "Pascal Vallet"
    },
    {
      "name": "Florent Bouchard"
    },
    {
      "name": "Guillaume Ginolhac"
    },
    {
      "name": "Audrey Giremus"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fp8cq86f4n6xb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18059",
  "fulltext_url": null,
  "id": "fp8cq86f4n6xb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18059",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7221795903",
  "pdf_url": "https://arxiv.org/pdf/2610.18059",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fp8cq86f4n6xb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.18059",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18059"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A new approach for estimating the number of spikes in high-dimensional Gaussian models",
  "title_text": "A new approach for estimating the number of spikes in high-dimensional Gaussian models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/fp8cq86f4n6xb",
  "venue": "arXiv",
  "versions": []
}