{
  "abstract": "We focus on the problem of estimating the average vector θ = (θ 1 , . . . , θ d ) of a random vector X ∈ R d which follows a spherically symmetric distribution. We consider modified balanced loss functions of the form:\n\nHere, δ 0 represents a target estimator of θ, ω ∈ [0, 1] and ρ and ℓ are increasing and concave functions. If d ≥ 4 and the target estimator is δ 0 (X) = X, we provide conditions on the parameter a for Baranchik type estimators δ a,S (X) = 1a(1 -ω)S( X 2 )/ X 2 X and reach the minimaxity. These conditions are derived using the radial properties of spherically symmetric distributions, which do not require the existence of a probability density for the random vector X. Furthermore, we extend the obtained results to the case of robust shrinkage estimators of the form δ ω,g (X) = X + a(1 -ω)g(X), where g(•) is a weakly differentiable and satisfying some conditions. Additionally, we conduct a simulation study in order to show the effectiveness and the usefulness of the obtained results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Lahoucine Hobbad"
    },
    {
      "name": "Mohamed Alahiane"
    },
    {
      "name": "Idir Ouassou"
    },
    {
      "name": "Mustapha Mr Rachdi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7n5shnap8pgzh.bib",
  "cited_by": 0,
  "doi": "10.22034/jirss.2025.2054911.1105",
  "fulltext_url": null,
  "id": "7n5shnap8pgzh",
  "issns": [
    "1726-4057",
    "2538-189X"
  ],
  "landing_url": "https://hal.science/hal-05756861v1",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-st"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7214395161",
  "pdf_url": "https://hal.science/hal-05756861/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": "The Iranian Statistical Society",
  "ris": "https://research.draconitic.com/paper/7n5shnap8pgzh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:36Z",
      "native_id": "hal-05756861",
      "source": "hal",
      "url": "https://hal.science/hal-05756861v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-st",
      "subfield": "statistics"
    }
  ],
  "title": "Shrinkage Estimation for Spherically Symmetric Distributions under Modified Balanced Loss Functions",
  "title_text": "Shrinkage Estimation for Spherically Symmetric Distributions under Modified Balanced Loss Functions",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:36Z",
  "url": "https://research.draconitic.com/paper/7n5shnap8pgzh",
  "venue": "Journal of The Iranian Statistical Society",
  "versions": []
}