Publicaciones de profesores y profesoras del Departamento de Matemática y Ciencias

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Browsing Publicaciones de profesores y profesoras del Departamento de Matemática y Ciencias by Issue Date

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    Resistant estimates for high dimensional and functional data based on random projections
    (2011) Fraiman, Ricardo; Svarc, Marcela
    We herein propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted contamination models, the procedure is robust and attains full efficiency. We tested the method using both simulated and real data.
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    Principal components for multivariate functional data
    (2011) Barrendero, J.R.; Justel, Ana; Svarc, Marcela
    A principal component method for multivariate functional data is proposed. Data can be arranged in a matrix whose elements are functions so that for each individual a vector of p functions is observed. This set of p curves is reduced to a small number of transformed functions, retaining as much information as possible. The criterion to measure the information loss is the integrated variance. Under mild regular conditions, it is proved that if the original functions are smooth this property is inherited by the principal components. A numerical procedure to obtain the smooth principal components is proposed and the goodness of the dimension reduction is assessed by two new measures of the proportion of explained variability. The method performs as expected in various controlled simulated data sets and provides interesting conclusions when it is applied to real data sets.
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    Interpretable Clustering using Unsupervised Binary Trees
    (2011) Fraiman, Ricardo; Ghattas, Badih; Svarc, Marcela
    We herein introduce a new method of interpretable clustering that uses unsupervised binary trees. It is a three-stage procedure, the rst stage of which entails a series of recursive binary splits to reduce the heterogeneity of the data within the new subsamples. During the second stage (pruning), consideration is given to whether adjacent nodes can be aggregated. Finally, during the third stage (joining), similar clusters are joined together, even if they do not share the same parent originally. Consistency results are obtained, and the procedure is used on simulated and real data sets.