<?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>0121-7488</journal-id>
<journal-title><![CDATA[Ciencia en Desarrollo]]></journal-title>
<abbrev-journal-title><![CDATA[Ciencia en Desarrollo]]></abbrev-journal-title>
<issn>0121-7488</issn>
<publisher>
<publisher-name><![CDATA[Universidad Pedagógica y Tecnológica de Colombia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-74882022000200099</article-id>
<article-id pub-id-type="doi">10.19053/01217488.v13.n2.2022.13650</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Testing for Normality in Geostatistics. A New Approach Based on the Mahalanobis Distance]]></article-title>
<article-title xml:lang="es"><![CDATA[A discussion on the use of univariate normality tests in this context]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Giraldo]]></surname>
<given-names><![CDATA[Ramón]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Porcu]]></surname>
<given-names><![CDATA[Emilio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia Department of Statistics ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Khalifa University Department of Mathematics ]]></institution>
<addr-line><![CDATA[Abu Dhabi ]]></addr-line>
<country>United Arab Emirates</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>13</volume>
<numero>2</numero>
<fpage>99</fpage>
<lpage>112</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-74882022000200099&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-74882022000200099&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-74882022000200099&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Simple kriging is a best linear predictor (BLP) and ordinary kriging is a best linear unbiased predictor (BLUP). When the underlying process is normal, simple kriging is not only a BLP but a best predictor (BT) as well, that is, under squared loss, this predictor coincides with the conditional expectation of the predictor given the information. In this scenario, ordinary kriging provides an approximation to the BP. For this reason, in applied geostatistics, it is important to test for normality. Given a realization of a spatial random process, the simple kriging predictor will be optimal if the random vector follows a multivariate normal distribution. Some classical tests, such as Shapiro-Wilk (SW), Shapiro-Francia (SF), or Anderson-Darling (AD) are frequently used to evaluate the normality assumption. Such approaches assume independence and hence are not effective for at least two reasons. On the one hand, observations in a geostatistical analysis are typically spatially correlated. On the other hand, kriging optimality as mentioned above is based on multivariate rather than univariate normality. In this work, we provide a simulation study to describe the negative effect of using normality univariate tests with geostatistical data. We also show how the Mahalanobis distance can be adapted to the geostatistical context to test for normality.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En geoestadística, bajo estacionariedad, kriging simple (KS) es el mejor predictor lineal (MPL) y kriging ordinario (KO) es el mejor predictor lineal insesgado (MPLI). Cuando el proceso estocástico es Normal, KS no es solo un MPL sino un mejor predictor (MP), es decir que bajo la función de perdida cuadrática, éste coincide con la esperanza condicional del predictor dada la información. En este escenario, el predictor KO sirve como aproximación del MP. Por esta razón, en geoestadística aplicada, es importante probar el supuesto de normalidad. Dada una realización de un proceso espacial, KS será un predictor óptimo si el vector aleatorio subyacente sigue una distribución normal multivariada. Algunas pruebas de normalidad clásicas como Shapiro-Wilk (SW), Shapiro-Francia (SF), o Anderson-Darling (AD) son usadas para evaluar este supuesto. Estas asumen independencia y por ello no son apropiadas en geoestadística (y en general en estadística espacial). Por un lado, las observaciones en geoestadística son espacialmente correlacionadas. Por otro lado la optimalidad del kriging es fundamentada en normalidad multivariada (no en normalidad univariada). En este trabajo se presenta un estudio de simulación para mostrar por qué es inapropiado el uso de pruebas univaridas de normalidad con datos geoestadísticos. También, como solución al problema anterior, se propone una adaptación de la prueba de Mahalanobis al contexto geoestadístico para hacer de manera correcta el test de normalidad en este arnbito.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Chi-square distribution]]></kwd>
<kwd lng="en"><![CDATA[Multivariate normal distribution]]></kwd>
<kwd lng="en"><![CDATA[Mahalanobis distance]]></kwd>
<kwd lng="en"><![CDATA[Normality test]]></kwd>
<kwd lng="en"><![CDATA[Random field]]></kwd>
<kwd lng="en"><![CDATA[Monte Carlo simulation]]></kwd>
<kwd lng="es"><![CDATA[Distribución chi-cuadrado]]></kwd>
<kwd lng="es"><![CDATA[Distribución normal multivariada]]></kwd>
<kwd lng="es"><![CDATA[Distancia de Mahalanobis]]></kwd>
<kwd lng="es"><![CDATA[Prueba de normalidad]]></kwd>
<kwd lng="es"><![CDATA[Campo aleatorio]]></kwd>
<kwd lng="es"><![CDATA[Simulación de Monte Carlo]]></kwd>
</kwd-group>
</article-meta>
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