<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04112846v2</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-19T14:22:20+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Asymptotic properties of continuous associated-kernel density estimators</title>
            <author role="aut">
              <persName>
                <forename type="first">Youssef</forename>
                <surname>Esstafa</surname>
              </persName>
              <email type="md5">d0b4fb0fe90e6cf8cb72403cb841681c</email>
              <email type="domain">univ-lemans.fr</email>
              <idno type="idhal" notation="string">youssefesstafa</idno>
              <idno type="idhal" notation="numeric">1143793</idno>
              <idno type="halauthorid" notation="string">2527802-1143793</idno>
              <idno type="ORCID">https://orcid.org/0009-0002-8880-9463</idno>
              <affiliation ref="#struct-90071"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Célestin</forename>
                <forename type="middle">C</forename>
                <surname>Kokonendji</surname>
              </persName>
              <idno type="halauthorid">2823206-0</idno>
              <affiliation ref="#struct-45"/>
              <affiliation ref="#struct-305454"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Thi-Bao-Trâm</forename>
                <surname>Ngô</surname>
              </persName>
              <idno type="halauthorid">2823207-0</idno>
              <affiliation ref="#struct-90071"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Youssef</forename>
                <surname>Esstafa</surname>
              </persName>
              <email type="md5">d0b4fb0fe90e6cf8cb72403cb841681c</email>
              <email type="domain">univ-lemans.fr</email>
            </editor>
            <funder ref="#projanr-57085"/>
            <funder ref="#projanr-50321"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2023-06-01 10:00:48</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2024-11-29 15:41:03</date>
              <date type="whenModified">2026-05-19 14:10:09</date>
              <date type="whenReleased">2024-12-05 15:46:17</date>
              <date type="whenProduced">2025</date>
              <date type="whenEndEmbargoed">2024-11-29</date>
              <ref type="file" target="https://hal.science/hal-04112846v2/document">
                <date notBefore="2024-11-29"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04112846v2/file/Asymptotic_properties_of_continuous_associated_kernel_density_estimators.pdf" id="file-4811572-4191604">
                <date notBefore="2024-11-29"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1087857">
                <persName>
                  <forename>Youssef</forename>
                  <surname>Esstafa</surname>
                </persName>
                <email type="md5">d0b4fb0fe90e6cf8cb72403cb841681c</email>
                <email type="domain">univ-lemans.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04112846</idno>
            <idno type="halUri">https://hal.science/hal-04112846</idno>
            <idno type="halBibtex">esstafa:hal-04112846</idno>
            <idno type="halRefHtml">&lt;i&gt;Communications in Statistics - Theory and Methods&lt;/i&gt;, 2025, &lt;a target="_blank" href="https://dx.doi.org/10.1080/03610926.2025.2530135"&gt;&amp;#x27E8;10.1080/03610926.2025.2530135&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Communications in Statistics - Theory and Methods, 2025, &amp;#x27E8;10.1080/03610926.2025.2530135&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4811572-4191604"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="AFRIQ">HAL-Francophonie, Afrique et océan indien</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-LEMANS">Université du Mans</idno>
            <idno type="stamp" n="LMM" corresp="UNIV-LEMANS">Laboratoire Manceau des Mathématiques</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="CHL">Centre Henri Lebesgue</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="LMB">Laboratoire de Mathématiques de Besançon (UMR 6623)</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Asymptotic properties of continuous associated-kernel density estimators</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Youssef</forename>
                    <surname>Esstafa</surname>
                  </persName>
                  <email type="md5">d0b4fb0fe90e6cf8cb72403cb841681c</email>
                  <email type="domain">univ-lemans.fr</email>
                  <idno type="idhal" notation="string">youssefesstafa</idno>
                  <idno type="idhal" notation="numeric">1143793</idno>
                  <idno type="halauthorid" notation="string">2527802-1143793</idno>
                  <idno type="ORCID">https://orcid.org/0009-0002-8880-9463</idno>
                  <affiliation ref="#struct-90071"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Célestin</forename>
                    <forename type="middle">C</forename>
                    <surname>Kokonendji</surname>
                  </persName>
                  <idno type="halauthorid">2823206-0</idno>
                  <affiliation ref="#struct-45"/>
                  <affiliation ref="#struct-305454"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Thi-Bao-Trâm</forename>
                    <surname>Ngô</surname>
                  </persName>
                  <idno type="halauthorid">2823207-0</idno>
                  <affiliation ref="#struct-90071"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">11917</idno>
                <idno type="issn">0361-0926</idno>
                <idno type="eissn">1532-415X</idno>
                <title level="j">Communications in Statistics - Theory and Methods</title>
                <imprint>
                  <publisher>Taylor &amp; Francis</publisher>
                  <date type="datePub">2025</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1080/03610926.2025.2530135</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Asymmetric kernel</term>
                <term xml:lang="en">Probability density function</term>
                <term xml:lang="en">Normalizing constant</term>
                <term xml:lang="en">Limit distribution</term>
                <term xml:lang="en">Convergence</term>
              </keywords>
              <classCode scheme="classification">MSC: Primary 62G07, 62G20; secondary 62G99.</classCode>
              <classCode scheme="halDomain" n="math.math-st">Mathematics [math]/Statistics [math.ST]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We consider the general modern notion of the so-called associated-kernels for smoothing density function on a given support. We first show that the unnormalized estimator is consistent and that the normalizing random variable converges in L^4 to 1. Then, we deduce the consistency of the considered normalized estimator. The comparison in favor of the normalized estimator is obtained by the mean squared error. We conclude by providing, for the first time, the general asymptotic normalities through some regularity assumptions for both unnormalized and normalized associated-kernel density estimators. The Gumbel, Weibull, lognormal, and other associated kernels are investigated for illustrating theoretically and numerically some of our results with an application to original data of automobile claim amounts from Covéa Affinity.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-90071" status="VALID">
          <idno type="IdRef">130408077</idno>
          <idno type="RNSR">200014561G</idno>
          <idno type="ROR">https://ror.org/037h7zx09</idno>
          <orgName>Laboratoire Manceau de Mathématiques</orgName>
          <orgName type="acronym">LMM</orgName>
          <desc>
            <address>
              <addrLine>Le Mans Université - Faculté des Sciences et TechniquesAvenue Olivier Messiaen - 72085 Le Mans Cedex 9 (France)</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation name="EA3263" active="#struct-7566" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-45" status="VALID">
          <idno type="IdRef">086229532</idno>
          <idno type="RNSR">197712394B</idno>
          <idno type="ROR">https://ror.org/04nrhwg12</idno>
          <orgName>Laboratoire de Mathématiques de Besançon (UMR 6623)</orgName>
          <orgName type="acronym">LMB</orgName>
          <date type="start">1996-01-01</date>
          <desc>
            <address>
              <addrLine>UFR Sciences et techniques 16 route de Gray 25 030 Besançon cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www-math.univ-fcomte.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR6623" active="#struct-441569" type="direct"/>
            <relation active="#struct-458810" type="direct"/>
            <relation active="#struct-426438" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-305454" status="VALID">
          <idno type="ROR">https://ror.org/020q46z35</idno>
          <orgName>Université de Bangui</orgName>
          <desc>
            <address>
              <addrLine>Avenue des Martyrs, Bangui</addrLine>
              <country key="CF"/>
            </address>
            <ref type="url">http://www.univ-bangui.org/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-7566" status="VALID">
          <idno type="IdRef">026404435</idno>
          <idno type="ROR">https://ror.org/01mtcc283</idno>
          <orgName>Le Mans Université</orgName>
          <orgName type="acronym">UM</orgName>
          <desc>
            <address>
              <addrLine>Avenue Olivier Messiaen - 72085 Le Mans cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lemans.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-458810" status="VALID">
          <idno type="IdRef">026403188</idno>
          <idno type="ISNI">0000000121883779</idno>
          <idno type="ROR">https://ror.org/03pcc9z86</idno>
          <orgName>Université Marie et Louis Pasteur</orgName>
          <orgName type="acronym">UMLP</orgName>
          <desc>
            <address>
              <addrLine>1 rue Goudimel25030 Besançon cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.umlp.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-426438" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-426438" status="VALID">
          <idno type="IdRef">200716271</idno>
          <idno type="ISNI">0000 0004 4910 6615</idno>
          <idno type="ROR">https://ror.org/02dn7x778</idno>
          <orgName>Université Bourgogne Franche-Comté [COMUE]</orgName>
          <orgName type="acronym">UBFC</orgName>
          <date type="start">2015-04-01</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>32, avenue de l’observatoire25000 BESANCON</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ubfc.fr</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-57085" status="VALID">
          <idno type="anr">ANR-21-CE40-0021</idno>
          <orgName>EFFI</orgName>
          <desc>Estimation efficace pour les données massives ou à haute-fréquence</desc>
          <date type="start">2021</date>
        </org>
        <org type="anrProject" xml:id="projanr-50321" status="VALID">
          <idno type="anr">ANR-17-EURE-0002</idno>
          <orgName>EIPHI</orgName>
          <desc>Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité</desc>
          <date type="start">2017</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>