<?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>0120-1751</journal-id>
<journal-title><![CDATA[Revista Colombiana de Estadística]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.Colomb.Estad.]]></abbrev-journal-title>
<issn>0120-1751</issn>
<publisher>
<publisher-name><![CDATA[Departamento de Estadística - Universidad Nacional de Colombia.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-17512006000200005</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[O princípio da equivariância: conceitos e aplicacões]]></article-title>
<article-title xml:lang="en"><![CDATA[The Principle of Equivariance: Concepts and Applications]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[NOBRE]]></surname>
<given-names><![CDATA[JUVÊNCIO]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[AZEVEDO]]></surname>
<given-names><![CDATA[CAIO]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidade de São Paulo Brasil e Instituto de Matemática e Estatística Universidade Federal do Ceará]]></institution>
<addr-line><![CDATA[São Paulo ]]></addr-line>
<country>Brasil</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidade de São Paulo Instituto de Matemática e Estatística ]]></institution>
<addr-line><![CDATA[São Paulo ]]></addr-line>
<country>Brasil</country>
</aff>
<pub-date pub-type="pub">
<day>05</day>
<month>12</month>
<year>2006</year>
</pub-date>
<pub-date pub-type="epub">
<day>05</day>
<month>12</month>
<year>2006</year>
</pub-date>
<volume>29</volume>
<numero>2</numero>
<fpage>195</fpage>
<lpage>220</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-17512006000200005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-17512006000200005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-17512006000200005&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Neste trabalho apresentamos uma revisão do princípio da estima,cão equivariante e algumas de suas aplicacões na família de localiza,cão-escala e em modelos lineares. Consideramos também o estimador não viciado de variância uniformemente mínima em modelos lineares. Vários exemplos são apresentados para ilustrar o uso destes métodos.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[In this work we present a review under the principle of equivariant estimation and their applications to the location-scale families and some linear models. We also consider the minimum variance unbiased estimation under the linear models framework. We show some examples to illustrate the use of those methods.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Estimacão equivariante]]></kwd>
<kwd lng="pt"><![CDATA[família de localiza,cão-escala]]></kwd>
<kwd lng="pt"><![CDATA[funcão de perda]]></kwd>
<kwd lng="pt"><![CDATA[modelos lineares]]></kwd>
<kwd lng="pt"><![CDATA[estimador não viciado de variância uniformemente mínima]]></kwd>
<kwd lng="en"><![CDATA[Equivariant estimation]]></kwd>
<kwd lng="en"><![CDATA[Location-scale families]]></kwd>
<kwd lng="en"><![CDATA[Loss function]]></kwd>
<kwd lng="en"><![CDATA[Linear models]]></kwd>
<kwd lng="en"><![CDATA[Minimum variance unbiased estimator]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[     <font size="2" face="verdana">        <p>    <center><b><font size="4">O princ&iacute;pio da equivari&acirc;ncia: conceitos e aplica,c&otilde;es</font></b></center></p>        <p>    <center><b><font size="3">The Principle of Equivariance: Concepts and Applications</font></b></center></p>        <p>    <center>JUV&Ecirc;NCIO NOBRE<sup>1</sup>, CAIO AZEVEDO<sup>2</sup></center></p>        <p><sup>1</sup> Departamento de Estat&iacute;stica e Matem&aacute;tica aplicada, Universidade Federal do Cear&aacute;, Forteleza, Brasil e Instituto de Matem&aacute;tica e Estat&iacute;stica, Universidade de S&atilde;o Paulo, S&atilde;o Paulo, Brasil, Professor assistente. E-mail: <a href="mailto:juvencio@ime.usp.br">juvencio@ime.usp.br</a>    <br>    <sup>2</sup> Instituto de Matem&aacute;tica e Estat&iacute;stica, Universidade de S&atilde;o Paulo, S&atilde;o Paulo, Brasil, Aluno de doutorado do curso de estat&iacute;stica. E-mail: <a href="mailto:cnaber@ime.usp.br">cnaber@ime.usp.br</a></p>    <hr size="1">        <p><b>    ]]></body>
<body><![CDATA[<center>Resumo</center></b></p>        <p>Neste trabalho apresentamos uma revis&atilde;o do princ&iacute;pio da estima,c&atilde;o equivariante e algumas de suas aplica,c&otilde;es na fam&iacute;lia de localiza,c&atilde;o-escala e em modelos lineares. Consideramos tamb&eacute;m o estimador n&atilde;o viciado de vari&acirc;ncia uniformemente m&iacute;nima em modelos lineares. V&aacute;rios exemplos s&atilde;o apresentados para ilustrar o uso destes m&eacute;todos.</p>        <p><b><i>Palavras chave:</i></b> Estima,c&atilde;o equivariante, fam&iacute;lia de localiza,c&atilde;o-escala, fun,c&atilde;o de perda, modelos lineares, estimador n&atilde;o viciado de vari&acirc;ncia uniformemente m&iacute;nima.</p>    <hr size="1">        <p><b>    <center>Abstract</center></b></p>        <p>In this work we present a review under the principle of equivariant estimation and their applications to the location-scale families and some linear models. We also consider the minimum variance unbiased estimation under the linear models framework. We show some examples to illustrate the use of those methods.</p>         <p><b><i>Key words:</i></b> Equivariant estimation, Location-scale families, Loss function, Linear models, Minimum variance unbiased estimator</p>    <hr size="1">        <p>Texto completo disponible en <a href="pdf/rce/v29n2/v29n2a05.pdf">PDF</a></p>    <hr size="1">        <p><b>REFER&Ecirc;NCIAS</b></p>        <!-- ref --><p>1. Alexander, T. L. &amp; Chandrasekar, B. (1999), &quot;Equivariant Estimation for the Para-  Meters of an Exponential Model Based on Censored Sampling&quot;, <i>Biometrical  Journal</i> <b>41</b>, 471- 481.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000022&pid=S0120-1751200600020000500001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>2. Borovkov, A. A. (1998), <i>Mathematics Statistics</i>, Gordon and Breach Science Publishes,  Moscow.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000023&pid=S0120-1751200600020000500002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>3. Casella, G. &amp; Berger, R. L. 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