Componentes principales robustas: una aplicación a localidades de la provincia de santa fe
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2014-11
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En este trabajo se presentó un análisis de componentes principales robusto a partir de los estimadores MM. Por otro lado, se consideró el método Bootstrap Rápido y Robusto para estimar intervalos de confianza para la proporción de variancia explicada de las componentes, y para calcular los límites de confianza de las cargas de las componentes principales robustas. Se desarrolló una aplicación de estos métodos a datos correspondientes a indicadores de carencias de comunas de la provincia de Santa Fe provenientes del Censo Nacional de Población, Hogares y Viviendas 2010, con el objetivo de lograr una estratificación de las mismas para un futuro marco de muestreo. A partir de la primera componente robusta se construyó un Índice de carencias, a partir del cual se estratificó a las comunas en cinco estratos a partir del método geométrico, el cual es apropiado para poblaciones asimétricas. Se observó que el estrato al cual pertenecen las comunas está relacionado con el nodo donde se encuentran ubicadas, encontrándose que a medida que uno se mueve de sur a norte en la provincia, las comunas tienden a tener mayores carencias
Principal components analysis (PCA) is a widely used technique within multivariate statistical methods. The purpose of this technique is adequately representing a set of n observations and p variables through fewer variables constructed as linear combinations of the original ones. It is based on the calculation of eigenvalues and eigenvectors of the covariance (or correlation) matrix. The presence of outliers in the data can distort the sample covariance matrix. Therefore various ways have been proposed to deal with this difficulty using robust techniques. The Bootstrap inference applied to classical robust estimators requires fewer assumptions but involves high computational cost and a loss of robustness in the presence of outliers. An alternative computationally simpler and more resistant to the presence of outliers is the Fast and Robust Bootstrap (FRB). The use of the robust principal components method and the robust bootstrap inference is illustrated on a dataset of indicators of critical needs of communes of the province of Santa Fe from the National Census Population and Housing 2010.
Principal components analysis (PCA) is a widely used technique within multivariate statistical methods. The purpose of this technique is adequately representing a set of n observations and p variables through fewer variables constructed as linear combinations of the original ones. It is based on the calculation of eigenvalues and eigenvectors of the covariance (or correlation) matrix. The presence of outliers in the data can distort the sample covariance matrix. Therefore various ways have been proposed to deal with this difficulty using robust techniques. The Bootstrap inference applied to classical robust estimators requires fewer assumptions but involves high computational cost and a loss of robustness in the presence of outliers. An alternative computationally simpler and more resistant to the presence of outliers is the Fast and Robust Bootstrap (FRB). The use of the robust principal components method and the robust bootstrap inference is illustrated on a dataset of indicators of critical needs of communes of the province of Santa Fe from the National Census Population and Housing 2010.
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Componentes Principales, Estimadores MM, Boostrap Rápido y Robusto, Boostrap