<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0123-7799</journal-id>
<journal-title><![CDATA[TecnoLógicas]]></journal-title>
<abbrev-journal-title><![CDATA[TecnoL.]]></abbrev-journal-title>
<issn>0123-7799</issn>
<publisher>
<publisher-name><![CDATA[Instituto Tecnológico Metropolitano - ITM]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0123-77992024000100207</article-id>
<article-id pub-id-type="doi">10.22430/22565337.2986</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Kruskal-Wallis Test for Functional Data Based on Random Projections Generated from a Simulation of a Brownian Motion]]></article-title>
<article-title xml:lang="es"><![CDATA[Prueba de Kruskal-Wallis para datos funcionales basada en proyecciones aleatorias generadas a partir de una simulación de un movimiento browniano]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Meléndez Surmay]]></surname>
<given-names><![CDATA[Rafael]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Giraldo Henao]]></surname>
<given-names><![CDATA[Ramón]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez Cortes]]></surname>
<given-names><![CDATA[Francisco]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de la Guajira  ]]></institution>
<addr-line><![CDATA[Riohacha ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[Medellín ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2024</year>
</pub-date>
<volume>27</volume>
<numero>59</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0123-77992024000100207&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0123-77992024000100207&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0123-77992024000100207&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The k-sample problem for functional data has been widely studied from theoretical and applied perspectives. In literature, Gaussianity of the generating process is generally assumed, which may be impractical in some situations. This work proposes an extension of the Kruskal-Wallis test to the case of functional data as an alternative to the problem of non-Gaussianity. The methodology used consisted of transforming each group's functional data into scalars using random projections and subsequently performing classical Kruskal-Wallis tests. The main results were the extension of the Kruskal-Wallis test to the case of functional data and the verification of its unbiased and consistency properties. Reducing dimensionality from random projections allows us to extend the classical Kruskal-Wallis test to the functional context and solve problems of non-Gaussianity and atypical observations.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El problema de k muestras de datos funcionales se ha estudiado ampliamente desde perspectivas teóricas y aplicadas. En la literatura se asume generalmente el supuesto de Gaussianidad del proceso generador, el cual puede ser impráctico en algunas situaciones particulares. Este trabajo tuvo como objetivo proponer una extensión de la prueba de Kruskal-Wallis al caso de datos funcionales, como alternativa al problema de no Gaussianidad. La metodología empleada consistió en transformar los datos funcionales de cada grupo en escalares empleando proyecciones aleatorias y en realizar posteriormente pruebas de Kruskal-Wallis clásicas. Los principales resultados fueron la extensión de la prueba de Kruskal-Wallis al caso de datos funcionales y la comprobación de las propiedades de insesgadez y consistencia de esta misma. Se puede concluir que la reducción de la dimensionalidad a partir de las proyecciones aleatorias permite extender la prueba de Kruskal-Wallis clásica al contexto funcional y por ende solucionar problemas de no Gaussianidad y observaciones atípicas.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Functional data]]></kwd>
<kwd lng="en"><![CDATA[Random projections]]></kwd>
<kwd lng="en"><![CDATA[Kruskal-Wallis test]]></kwd>
<kwd lng="en"><![CDATA[Non-parametric statistics]]></kwd>
<kwd lng="en"><![CDATA[Brownian motion]]></kwd>
<kwd lng="es"><![CDATA[Datos funcionales]]></kwd>
<kwd lng="es"><![CDATA[Proyecciones aleatorias]]></kwd>
<kwd lng="es"><![CDATA[Prueba de Kruskal-Wallis]]></kwd>
<kwd lng="es"><![CDATA[Estadística no paramétrica]]></kwd>
<kwd lng="es"><![CDATA[Movimiento Browniano]]></kwd>
</kwd-group>
</article-meta>
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<name>
<surname><![CDATA[Pohlert]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Pairwise Multiple Comparison of Mean Ranks Package (PMCMR) v4.4. 2016.]]></source>
<year>2023</year>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
