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 Statistics , 2012, DOI: 10.3150/13-BEJ564 Abstract: The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We suppose that we have at our disposal two learning samples. The aim is to approach the best possible decision rule $G^\star$ defined as a minimizer of the Bayes risk. In the free-noise case $(\epsilon=0)$, minimax fast rates of convergence are well-known under the margin assumption in discriminant analysis (see \cite{mammen}) or in the more general classification framework (see \cite{tsybakov2004,AT}). In this paper we intend to establish similar results in the noisy case, i.e. when dealing with errors in variables. We prove minimax lower bounds for this problem and explain how can these rates be attained, using in particular an Empirical Risk Minimizer (ERM) method based on deconvolution kernel estimators.
 Jesús Yoel Crespo Ecos de Economía , 2011, Abstract: El artículo presentan las calificaciones de riesgo de las instituciones pertenecientes al sistema financiero venezolano al cierre del primer semestre del a o 2010, obtenidas mediante la aplicación de dos metodologías: la primera conocida como CAMEL y la segunda a través de una técnica estadística denominada análisis discriminante, esta última permitirá clasificar a las instituciones financieras en categorías de riesgo, formar un perfil que muestre las característica más representativa de las categoría y cuantificar la probabilidad de pertenecer a una calificación. La investigación pretende establecer si un modelo es mejor que el otro, sino demostrar que se puede complementar el análisis netamente descriptivo con el análisis multivariante, aplicándolo en un área del saber que ha sido poco explotada en Venezuela, permitiendo informar a la colectividad en general, las técnicas estadísticas empleadas en materia de riesgo. Abstract This paper presents the credit ratings of the institutions belonging to the Venezuelan financial system at the end of the first half of 2010, obtained by applying two methods: the first known as CAMEL and the second through a statistical technique called analysis discriminant, the latter will qualify for financial institutions in risk categories, form a profile that shows the most representative feature of the category and quantify the probability of belonging to a rating. This research does not establish whether one model is better than the other, but show that you can supplement purely descriptive analysis multivariate analysis, applied to an area of knowledge that has been little exploited in Venezuela, allowing to inform the public at large , the statistical techniques used in risk. This paper presents the credit ratings of the institutions belonging to the Venezuelanfinancial system at the end of the first half of 2010, obtained by applying two methods:the first known as CAMEL and the second through a statistical technique called analysisdiscriminant, the latter will qualify for financial institutions in risk categories, form aprofile that shows the most representative feature of the category and quantify theprobability of belonging to a rating.This research does not establish whether one model is better than the other, but showthat you can supplement purely descriptive analysis multivariate analysis, applied toan area of knowledge that has been little exploited in Venezuela, allowing to inform thepublic at large , the statistical techniques used in risk.