<?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>0121-1935</journal-id>
<journal-title><![CDATA[Revista de Ciencias]]></journal-title>
<abbrev-journal-title><![CDATA[rev. cienc.]]></abbrev-journal-title>
<issn>0121-1935</issn>
<publisher>
<publisher-name><![CDATA[Universidad del Valle]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-19352016000200039</article-id>
<article-id pub-id-type="doi">10.25100/rc.v20i2.4672</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Método BFGS estructurado para la estimación de máxima verosimilitud]]></article-title>
<article-title xml:lang="en"><![CDATA[Structured BFGS Method for the Estimation of the Maximum Likelihood]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Arenas]]></surname>
<given-names><![CDATA[Favián]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[Héctor Jairo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pérez]]></surname>
<given-names><![CDATA[Rosana]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Cauca Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Popayán ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad del Valle Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<volume>20</volume>
<numero>2</numero>
<fpage>39</fpage>
<lpage>54</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-19352016000200039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-19352016000200039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-19352016000200039&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Teniendo en cuenta la estructura especial de la matriz hessiana del logaritmo de la función de verosimilitud análoga a la estructura encontrada en problemas de mínimos cuadrados no lineales, se propone el método BFGS estructurado para el problema de la estimación de máxima verosimilitud y se desarrolla su teoría de convergencia local y q-superlineal siguiendo los lineamientos generales de la teoría de convergencia desarrollada en Martínez; Martínez y Egels para métodos secante estructurados y la teoría sobre estimación de la máxima verosimilitud dada en Gonglewski. Además, se realizaron pruebas numéricas preliminares que muestran el buen comportamiento local del método propuesto.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Given the special structure of the Hessian matrix of the log-likelihood function which is parallel to that found in nonlinear least-squares problems, we introduce the structured BFGS secant method for the maximum-likelihood estimation and for the development or the local and super-linear convergence theory for the algorithm, following the lines of Martínez; Martínez and Egels, and the theory about maximum-likelihood estimation given in Gonglewski. We present the results of some numerical experiments which show a good performance of our algorithm.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Estimación de máxima verosimilitud]]></kwd>
<kwd lng="es"><![CDATA[función de verosimilitud]]></kwd>
<kwd lng="es"><![CDATA[método secante estructurado]]></kwd>
<kwd lng="es"><![CDATA[mínimos cuadrados no lineales]]></kwd>
<kwd lng="es"><![CDATA[convergencia super lineal]]></kwd>
<kwd lng="en"><![CDATA[maximum likelihood estimation]]></kwd>
<kwd lng="en"><![CDATA[likelihood function]]></kwd>
<kwd lng="en"><![CDATA[structured secant method]]></kwd>
<kwd lng="en"><![CDATA[nonlinear least&#8208;squares problem]]></kwd>
<kwd lng="en"><![CDATA[super-linear convergence]]></kwd>
</kwd-group>
</article-meta>
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