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Master's Dissertation
DOI
10.11606/D.45.2011.tde-21052012-170807
Document
Author
Full name
André Pierro de Camargo
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Lauretto, Marcelo de Souza (President)
Salinas, Delhi Teresa Paiva
Stern, Julio Michael
Title in Portuguese
Modelos de regressão sobre dados composicionais
Keywords in Portuguese
BIC
Dados composicionais
FBST
Modelos de regressão
Seleção de modelos
Abstract in Portuguese
Dados composicionais são constituídos por vetores cujas componentes representam as proporções de algum montante, isto é: vetores com entradas positivas cuja soma é igual a 1. Em diversas áreas do conhecimento, o problema de estimar as partes $y_1, y_2, \dots, y_D$ correspondentes aos setores $SE_1, SE_2, \dots, SE_D$, de uma certa quantidade $Q$, aparece com frequência. As porcentagens $y_1, y_2, \dots, y_D$ de intenção de votos correspondentes aos candidatos $Ca_1, Ca_2, \dots, Ca_D$ em eleições governamentais ou as parcelas de mercado correspondentes a industrias concorrentes formam exemplos típicos. Naturalmente, é de grande interesse analisar como variam tais proporções em função de certas mudanças contextuais, por exemplo, a localização geográfica ou o tempo. Em qualquer ambiente competitivo, informações sobre esse comportamento são de grande auxílio para a elaboração das estratégias dos concorrentes. Neste trabalho, apresentamos e discutimos algumas abordagens propostas na literatura para regressão sobre dados composicionais, assim como alguns métodos de seleção de modelos baseados em inferência bayesiana. \\
Title in English
Regression model for Compositional data
Keywords in English
BIC
Compositional data
FBST
Model selection
Regression models
Abstract in English
Compositional data consist of vectors whose components are the proportions of some whole. The problem of estimating the portions $y_1, y_2, \dots, y_D$ corresponding to the pieces $SE_1, SE_2, \dots, SE_D$ of some whole $Q$ is often required in several domains of knowledge. The percentages $y_1, y_2, \dots, y_D$ of votes corresponding to the competitors $Ca_1, Ca_2, \dots, Ca_D$ in governmental elections or market share problems are typical examples. Of course, it is of great interest to study the behavior of such proportions according to some contextual transitions. In any competitive environmet, additional information of such behavior can be very helpful for the strategists to make proper decisions. In this work we present and discuss some approaches proposed by different authors for compositional data regression as well as some model selection methods based on bayesian inference.\\
 
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Publishing Date
2012-05-22
 
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