Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "12775"
  #_source: array:26 [
    "id" => "12775"
    "slug" => "multi-normex-distributions-for-the-sum-of-random-vectors-rates-of-convergence"
    "yearMonth" => "2021-07"
    "year" => "2021"
    "title" => "Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence"
    "description" => "KRATZ, M. et PROKOPENKO, E. (2021). <i>Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence</i>. 2102, ESSEC Business School."
    "authors" => array:2 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
      1 => array:1 [
        "name" => "PROKOPENKO Evgeny"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:12 [
      0 => "aggregation"
      1 => "central limit theorem"
      2 => "dependence"
      3 => "extreme value theorem"
      4 => "geometrical quantiles"
      5 => "multivariate regular variation"
      6 => "(multivariate) Pareto distribution"
      7 => "ordered statistics"
      8 => "QQ-plots"
      9 => "rate of convergence"
      10 => "second order regular variation"
      11 => "sum of random vectors"
    ]
    "updatedAt" => "2023-01-27 01:00:41"
    "publicationUrl" => null
    "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 build a sharp approximation of the whole distribution of the sum of iid heavy-tailed - random vectors, combining mean and extreme behaviors. It extends the so-called ’normex’ - approach from a univariate to a multivariate framework. We propose two possible multinormex - distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distribution - for describing the mean behavior, via the CLT, while the difference between the - two versions comes from using the exact distribution or the EV theorem for the maximum. - The main theorems provide the rate of convergence for each version of the multi-normex - distributions towards the distribution of the sum, assuming second order regular variation - property for the norm of the parent random vector when considering the MRV-normex - case. Numerical illustrations and comparisons are proposed with various dependence structures - on the parent random vector, using QQ-plots based on geometrical quantiles."
      "en" => "We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed - random vectors, combining mean and extreme behaviors. It extends the so-called ’normex’ - approach from a univariate to a multivariate framework. We propose two possible multinormex - distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distribution - for describing the mean behavior, via the CLT, while the difference between the - two versions comes from using the exact distribution or the EV theorem for the maximum. - The main theorems provide the rate of convergence for each version of the multi-normex - distributions towards the distribution of the sum, assuming second order regular variation - property for the norm of the parent random vector when considering the MRV-normex - case. Numerical illustrations and comparisons are proposed with various dependence structures - on the parent random vector, using QQ-plots based on geometrical quantiles."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-12-03T16:21:42.000Z"
    "docTitle" => "Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence"
    "docSurtitle" => "Working Papers"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>, PROKOPENKO Evgeny"
    "docDescription" => "<span class="document-property-authors">KRATZ Marie, PROKOPENKO Evgeny</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2021</span>"
    "keywordList" => "<a href="#">aggregation</a>, <a href="#">central limit theorem</a>, <a href="#">dependence</a>, <a href="#">extreme value theorem</a>, <a href="#">geometrical quantiles</a>, <a href="#">multivariate regular variation</a>, <a href="#">(multivariate) Pareto distribution</a>, <a href="#">ordered statistics</a>, <a href="#">QQ-plots</a>, <a href="#">rate of convergence</a>, <a href="#">second order regular variation</a>, <a href="#">sum of random vectors</a>"
    "docPreview" => "<b>Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence</b><br><span>2021-07 | Working Papers </span>"
    "docType" => "research"
    "publicationLink" => "<a href="#" target="_blank">Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence</a>"
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 8.099655
  +"parent": null
}