Resistant estimates for high dimensional and functional data based on random projections

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.Comment: 24 pages, 6 figure

Resistant estimates for high dimensional and functional data based on random projections

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.Fil: Fraiman, Jacob Ricardo. Universidad de San Andrés; Argentina. Universidad de la República; Uruguay. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Svarc, Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; Argentin

Interpretable Clustering using Unsupervised Binary Trees

We herein introduce a new method of interpretable clustering that uses unsupervised binary trees. It is a three-stage procedure, the first 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 descend from the same node originally. Consistency results are obtained, and the procedure is used on simulated and real data sets.Comment: 25 pages, 6 figure

Feature Selection for Functional Data

In this paper we address the problem of feature selection when the data is functional, we study several statistical procedures including classification, regression and principal components. One advantage of the blinding procedure is that it is very flexible since the features are defined by a set of functions, relevant to the problem being studied, proposed by the user. Our method is consistent under a set of quite general assumptions, and produces good results with the real data examples that we analyze.Comment: 22 pages, 4 figure

Selection of variables for cluster analysis and classification rules

In this paper we introduce two procedures for variable selection in cluster analysis and classification rules. One is mainly oriented to detect the noisy non-informative variables, while the other deals also with multicolinearity. A forward-backward algorithm is also proposed to make feasible these procedures in large data sets. A small simulation is performed and some real data examples are analyzed.Comment: 28 pages, 7 figure

Deprivation and the dimmensionality of welfare: a variable-selection cluster analysis approach

En este artículo abordamos los problemas de la dimensionalidad del bienestar y el de la identificación de los pobres en forma multidimensional, encontrando primero los pobres con el espacio original de atributos, y luego reduciendo el espacio de bienestar. El punto de partida es la idea de que los "pobres" constituyen un grupo de individuos que son esencialmente diferentes de los "no pobres" en un marco multidimensional. Una vez que este grupo ha sido identificado, se propone reducir la dimensión del espacio de bienestar original resolviendo el problema de encontrar el más pequeño conjunto de atributos que se pueden reproducir con la mayor precisión posible para clasificar a los "pobres/no pobres" en la primera etapa.Centro de Estudios Distributivos, Laborales y Sociales (CEDLAS

Deprivation and the dimmensionality of welfare: a variable-selection cluster analysis approach

En este artículo abordamos los problemas de la dimensionalidad del bienestar y el de la identificación de los pobres en forma multidimensional, encontrando primero los pobres con el espacio original de atributos, y luego reduciendo el espacio de bienestar. El punto de partida es la idea de que los "pobres" constituyen un grupo de individuos que son esencialmente diferentes de los "no pobres" en un marco multidimensional. Una vez que este grupo ha sido identificado, se propone reducir la dimensión del espacio de bienestar original resolviendo el problema de encontrar el más pequeño conjunto de atributos que se pueden reproducir con la mayor precisión posible para clasificar a los "pobres/no pobres" en la primera etapa.Centro de Estudios Distributivos, Laborales y Sociales (CEDLAS

Deprivation and the dimmensionality of welfare: a variable-selection cluster analysis approach

En este artículo abordamos los problemas de la dimensionalidad del bienestar y el de la identificación de los pobres en forma multidimensional, encontrando primero los pobres con el espacio original de atributos, y luego reduciendo el espacio de bienestar. El punto de partida es la idea de que los "pobres" constituyen un grupo de individuos que son esencialmente diferentes de los "no pobres" en un marco multidimensional. Una vez que este grupo ha sido identificado, se propone reducir la dimensión del espacio de bienestar original resolviendo el problema de encontrar el más pequeño conjunto de atributos que se pueden reproducir con la mayor precisión posible para clasificar a los "pobres/no pobres" en la primera etapa.Centro de Estudios Distributivos, Laborales y Sociales (CEDLAS

The choice of inicial Estimate for Computing MM-Estimates

Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.We show, using a Monte Carlo study, that MM-estimates with projec- tion estimates as starting point of an iterative weighted least squares algorithm, behave more robustly than MM-estimates starting at an S-estimate and similar Gaussian efficiency. Moreover the former have a robustness behavior close to the P-estimates with an additional advantage: they are asymptotically normal making statistical inference possible

Pattern recognition via projection – based k – NN rules

Fil: Fraiman, Ricardo. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.Fil: Justel, Ana. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.We introduce a new procedure for pattern recognition, based on the concepts of random projections and nearest neighbors. It can be thought as an improvement of the classical nearest neighbors classification rules. Besides the concept of neighbors we introduce the notion of district, a larger set which will be projected. Then we apply one dimensional k-NN methods to the projected data on randomly selected directions. In this way we are able to provide a method with some robustness properties and more accurate to handle high dimensional data. The procedure is also universally consistent. We challenge the method with the Isolet data where we obtain a very high classification score