Essec\Faculty\Model\Contribution {#2233
  #_index: "academ_contributions"
  #_id: "15177"
  #_source: array:26 [
    "id" => "15177"
    "slug" => "15177-from-geometric-quantiles-to-halfspace-depths-a-geometric-approach-for-extremal-behaviour"
    "yearMonth" => "2023-06"
    "year" => "2023"
    "title" => "From geometric quantiles to halfspace depths: A geometric approach for extremal behaviour"
    "description" => "SINGHA, S., KRATZ, M. et VADLAMANI, S. (2023). <i>From geometric quantiles to halfspace depths: A geometric approach for extremal behaviour</i>. WP 2307, ESSEC Business School."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
      1 => array:1 [
        "name" => "SINGHA Sibsankar"
      ]
      2 => array:1 [
        "name" => "VADLAMANI Sreekar"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:6 [
      0 => "asymptotic theorems"
      1 => "concentration inequality"
      2 => "halfspace (or Tukey) depth -empirical process"
      3 => "extreme quantile"
      4 => "geometric quantile"
      5 => "multivariate quantile -tail behaviour"
    ]
    "updatedAt" => "2025-03-17 16:58:41"
    "publicationUrl" => "https://essec.hal.science/hal-04134321"
    "publicationInfo" => array:3 [
      "pages" => ""
      "volume" => ""
      "number" => ""
    ]
    "type" => array:2 [
      "fr" => "Documents de travail"
      "en" => "Working Papers"
    ]
    "support_type" => array:2 [
      "fr" => "Cahier de Recherche"
      "en" => "Working Papers"
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => "We investigate the asymptotics for two geometric measures, geometric quantiles and halfspace depths. While much literature is known on the population side, we fill out some gaps there to obtain a full picture, before turning to the sample versions, where the questions on asymptotics become crucial in view of applications. This is the core of the paper: We provide rates of convergence for the sample versions and address the extremal behaviour of the geometric measures according to the type of underlying distribution."
      "en" => "We investigate the asymptotics for two geometric measures, geometric quantiles and halfspace depths. While much literature is known on the population side, we fill out some gaps there to obtain a full picture, before turning to the sample versions, where the questions on asymptotics become crucial in view of applications. This is the core of the paper: We provide rates of convergence for the sample versions and address the extremal behaviour of the geometric measures according to the type of underlying distribution."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2025-07-20T12:21:43.000Z"
    "docTitle" => "From geometric quantiles to halfspace depths: A geometric approach for extremal behaviour"
    "docSurtitle" => "Documents de travail"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>, SINGHA Sibsankar, VADLAMANI Sreekar"
    "docDescription" => "<span class="document-property-authors">KRATZ Marie, SINGHA Sibsankar, VADLAMANI Sreekar</span><br><span class="document-property-authors_fields">Systèmes d'Information, Data Analytics et Opérations</span> | <span class="document-property-year">2023</span>"
    "keywordList" => "<a href="#">asymptotic theorems</a>, <a href="#">concentration inequality</a>, <a href="#">halfspace (or Tukey) depth -empirical process</a>, <a href="#">extreme quantile</a>, <a href="#">geometric quantile</a>, <a href="#">multivariate quantile -tail behaviour</a>"
    "docPreview" => "<b>From geometric quantiles to halfspace depths: A geometric approach for extremal behaviour</b><br><span>2023-06 | Documents de travail </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://essec.hal.science/hal-04134321" target="_blank">From geometric quantiles to halfspace depths: A geometric approach for extremal behaviour</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 8.658067
  +"parent": null
}