<?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>1794-9165</journal-id>
<journal-title><![CDATA[Ingeniería y Ciencia]]></journal-title>
<abbrev-journal-title><![CDATA[ing.cienc.]]></abbrev-journal-title>
<issn>1794-9165</issn>
<publisher>
<publisher-name><![CDATA[Escuela de Ciencias y Humanidades y Escuela de Ingeniería de la Universidad EAFIT]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1794-91652020000100077</article-id>
<article-id pub-id-type="doi">10.17230/ingciencia.16.31.4</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Diseños D&#960;-óptimos para modelos no lineales heteroscedásticos: Un estudio de robustez]]></article-title>
<article-title xml:lang="en"><![CDATA[D&#960; -optimal Designs for Heteroscedastic Nonlinear Models: A Robustness Study]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Patiño-Bustamante]]></surname>
<given-names><![CDATA[Catalina]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[López-Ríos]]></surname>
<given-names><![CDATA[Víctor]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[Medellín ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<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>06</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2020</year>
</pub-date>
<volume>16</volume>
<numero>31</numero>
<fpage>77</fpage>
<lpage>101</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S1794-91652020000100077&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S1794-91652020000100077&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S1794-91652020000100077&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Los diseños óptimos son utilizados para determinar las mejores condiciones donde se debe realizar un experimento para obtener ciertas propiedades estadísticas. En los modelos no lineales heteroscedásticos donde la varianza es una función de la media, el criterio de optimalidad depende de la elección de un valor local para los parámetros del modelo. Una forma de evitar esta dependencia es considerar una distribución a priori para el vector de parámetros del modelo e incorporarla en el criterio de optimalidad que se va a optimizar. En este artículo se consideran diseños D-óptimos en modelos no lineales heteroscedásticos cuando se incorpora una distribución a priori asociada a los parámetros del modelo. Se extiende el teorema de equivalencia al considerar el efecto de la distribución a priori. Se propone una metodología para la construcción de distribuciones a priori discretas y continuas. Se muestra, con un ejemplo, cómo a partir de las distribuciones construidas se pueden encontrar diseños óptimos con mayor número de puntos experimentales que los obtenidos con un valor local. La eficiencia de los diseños hallados es muy competitiva comparada con los diseños óptimos locales. Adicionalmente se consideran distribuciones a priori de una familia de escala, y se muestra que los diseños hallados son robustos a la elección de la distribución a priori elegida de esta familia.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Optimal designs are used to determine the best conditions where an experiment should be performed to obtain certain statistical properties. In heteroscedastic nonlinear models where variance is a function of the mean, the optimality criterion depends on the choice of a local value for the model parameters. One way to avoid this dependency is to consider an a priori distribution for the vector of model parameters and incorporate it into the optimality criterion to be optimized. This paper considers D -optimal designs in heteroscedastic nonlinear models when a prior distribution associated with the model parameters is incorporated. The equivalence theorem is extended by considering the effect of the prior distribution. A methodology for the construction of discrete and continuous prior distributions is proposed. It is shown, with an example, how optimal designs can be found from the constructed distributions with a greater number of experimental points than those obtained with a local value. The efficiency of the designs found is very competitive compared to the optimal local designs. Additionally, prior distributions of a scale family are considered, and it is shown that the designs found are robust to the choice of the prior distribution chosen from this family.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Diseños óptimos]]></kwd>
<kwd lng="es"><![CDATA[matriz de información]]></kwd>
<kwd lng="es"><![CDATA[teorema de equivalencia]]></kwd>
<kwd lng="es"><![CDATA[distribuciones a priori]]></kwd>
<kwd lng="es"><![CDATA[modelos heteroscedásticos]]></kwd>
<kwd lng="en"><![CDATA[Optimal designs]]></kwd>
<kwd lng="en"><![CDATA[information matrix]]></kwd>
<kwd lng="en"><![CDATA[equivalence theorem]]></kwd>
<kwd lng="en"><![CDATA[prior distribution]]></kwd>
<kwd lng="en"><![CDATA[heteroscedastic models]]></kwd>
</kwd-group>
</article-meta>
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<given-names><![CDATA[S.]]></given-names>
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<article-title xml:lang=""><![CDATA[Robust wild bootstrap for stabilizing the variance of parameter estimates in heteroscedastic regression models in the presenceof outliers]]></article-title>
<source><![CDATA[Mathematical Problems in Engineering]]></source>
<year>2012</year>
<volume>95</volume>
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</article>
