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Variable selection in linear regression models with large number of predictors

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Resumo:In this thesis, we study the problem of variable selection in linear regression models in the presence of a large number of predictors. Usually, some of these predictors are correlated, so including all of them in a regression model will not essentially improve the model's predictive ability. Also, models with reasonable and tractable amount of predictors are easier to interpret than models with a large number of predictors. Therefore, variable selection is an important problem to study. Given that there are some popular regression methods capable of handling collinearity in data but still requiring the removal of irrelevant predictors, so we present an algorithm that enable these methods to perform variable selection. We review the well-known variable selection methods, and investigate the performance of these methods as well as the proposed approach on both simulated and real data sets. The results show that the new algorithm performs well in selecting the relevant variables. Also, when the data contains outliers, outlier detection and variable selection are not two separable problems. Therefore, we propose a method capable of outlier detection and variable selection. We review the well-known robust variable selection methods and evaluate the performance of these methods with the proposed approach on contaminated simulation data sets as well as on real data. The results show that the proposed method performs well concerning both outlier detection and robust variable selection.
Autores principais:Shahriari, Shirin
Assunto:Bootstrap Least angle regression (LARS) Linear regression Partial least squares regression (PLSR) Outlier detection Variable selection Deteção de outliers Principal components regression (PCR) Regressão linear Seleção de variáveis
Ano:2014
País:Portugal
Tipo de documento:tese de doutoramento
Tipo de acesso:acesso aberto
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

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