Essec\Faculty\Model\Contribution {#6196`
#_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, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
`]
"indexedAt" => "2024-02-22T08:22:00.000Z"
"docTitle" => "Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence"
"docSurtitle" => "Documents de travail"
"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">Systèmes d’Information, Sciences de la Décision et Statistiques</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 | Documents de travail </span>"
"docType" => "research"
"publicationLink" => "<a href="#" target="_blank">Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence</a>"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 8.387085
+"parent": null
}