Depth-based inference for functional data

We propose robust inference tools for functional data based on the notion of depth for curves. We extend the ideas of trimmed regions, contours and central regions to functions and study their structural properties and asymptotic behavior. Next, we introduce a scale curve to describe dispersion in a sample of functions. The computational burden of these techniques is not heavy and so they are also adequate to analyze high-dimensional data. All these inferential methods are applied to different real data sets

Depth-based classification for functional data

Classification is an important task when data are curves. Recently, the notion of statistical depth has been extended to deal with functional observations. In this paper, we propose robust procedures based on the concept of depth to classify curves. These techniques are applied to a real data example. An extensive simulation study with contaminated models illustrates the good robustness properties of these depth-based classification methods

On the concept of depth for functional data

The statistical analysis of functional data is a growing need in many research areas. We propose a new depth notion for functional observations based on the graphic representation of the curves. Given a collection of functions, it allows to establish the centrality of a function and provides a natural center-outward ordering of the sample curves. Robust statistics such as the median function or a trimmed mean function can be defined from this depth definition. Its finite-dimensional version provides a new depth for multivariate data that is computationally very fast and turns out to be convenient to study high-dimensional observations. The natural properties are established for the new depth and the uniform consistency of the sample depth is proved. Simulation results show that the trimmed mean presents a better behavior than the mean for contaminated models. Several real data sets are considered to illustrate this new concept of depth. Finally, we use this new depth to generalize to functions the Wilcoxon rank sum test. It allows to decide whether two groups of curves come from the same population. This functional rank test is applied to girls and boys growth curves concluding that they present different growth patterns

Simplicial similarity and its application to hierarchical clustering

In the present document, an extension of the statistical depth notion is introduced with the aim to allow for measuring proximities between pairs of points. In particular, we will extend the simplicial depth function, which measures how central is a point by using random simplices (triangles in the two-dimensional space). The paper is structured as follows: In first place, there is a brief introduction to statistical depth functions. Next, the simplicial similarity function will be defined and its properties studied. Finally, we will present a few graphical examples in order to show its behavior with symmetric and asymmetric distributions, and apply the function to hierarchical clustering.Statistical depth, Similarity measures, Hierarchical clustering

A half-graph depth for functional data

A recent and highly attractive area of research in statistics is the analysis of functional data. In this paper a new definition of depth for functional observations is introduced based on the notion of "half-graph" of a curve. It has computational advantages with respect to other concepts of depth previously proposed. The half-graph depth provides a natural criterion to measure the centrality of a function within a sample of curves. Based on this depth a sample of curves can be ordered from the center outward and L-statistics are defined. The properties of the half-graph depth, such as the consistency and uniform convergence, are established. A simulation study shows the robustness of this new definition of depth when the curves are contaminated. Finally real data examples are analyzed

Simplicial similarity and its application to hierarchical clustering

In the present document, an extension of the statistical depth notion is introduced with the aim to allow for measuring proximities between pairs of points. In particular, we will extend the simplicial depth function, which measures how central is a point by using random simplices (triangles in the two-dimensional space). The paper is structured as follows: In first place, there is a brief introduction to statistical depth functions. Next, the simplicial similarity function will be defined and its properties studied. Finally, we will present a few graphical examples in order to show its behavior with symmetric and asymmetric distributions, and apply the function to hierarchical clustering

A half-region depth for functional data.

A new definition of depth for functional observations is introduced based on the notion of “half-region” determined by a curve. The half-regiondepth provides a simple and natural criterion to measure the centrality of a function within a sample of curves. It has computational advantages relative to other concepts of depth previously proposed in the literature which makes it applicable to the analysis of high-dimensional data. Based on this deptha sample of curves can be ordered from the center-outward and order statistics can be defined. The properties of the half-regiondepth, such as consistency and uniform convergence, are established. A simulation study shows the robustness of this new definition of depth when the curves are contaminated. Finally, real data examples are analyzed.This research was partially supported by Spanish Ministry of Education and Science grants BEC 2002-03769, SEJ2005-06454, SEJ2007-67734, SEJ2905 and ECO2008-05080.Publicad

Actitudes hacia la salud holística, complementaria y alternativa

La medicina complementaria y alternativa es comprendida como el conjunto de conocimientos, aptitudes y prácticas que son utilizadas para la prevención, diagnóstico y tratamiento de enfermedades físicas y mentales, basándose en las experiencias de los pueblos originarios en todo el mundo, es decir en los conocimientos ancestrales.  Con este antecedente el presente estudio tiene por finalidad determinar las actitudes hacia la salud holística, complementaria y alternativa de los habitantes de la comunidad Chambapongo, del Cantón Salcedo en la Provincia de Cotopaxi. Para el mismo se aplicó una metodología con enfoque cuantitativa, no experimental, transversal y de campo el instrumento de recolección de datos fue el formulario de medicina alternativa y complementaria, Holistic Complementary and Alternative Medicine Questionnaire (HCAMQ), tras la aplicación del mismo se realizó un análisis de los resultados obtenidos con el fin de  Se puede concluir mediante los resultados obtenidos y análisis de los mismos que los moradores de la comunidad de Chambapongo tienen una actitud  positiva hacia el uso de la medicina holística, complementaria y alternativa evidenciándose una mayor acogida en el ámbito no farmacológico para el manejo de enfermedades comunes

Creencias, tabúes y mitos en relación con la lactancia materna: Crenças, tabus e mitos sobre a amamentação

En los últimos decenios, diversos factores han dado lugar a mitos, creencias y tabúes respecto del manejo de la lactancia materna (LM), los cuales se asocian al abandono de la LM en los meses más importantes para el desarrollo del niño. Por ello, el objetivo del presente trabajo fue realizar un análisis comparativo entre  las percepciones y lo que indica  la comunidad científica respecto a las creencias, tabúes y mitos en relación con la lactancia materna, en madres del cantón Tisaleo, provincia de Tungurahua, para conocer las distintas experiencias y promover una adecuada educación a través de un blog informativo.La metodología empleó un enfoque cualitativo, con alcance descriptivo y transversal, para lo cual se consideró a las madres que se encontraban dando de lactar, independientemente de la edad. El instrumento empleado fue la entrevista semiestructurada por categorías, tomada de Demazière y Dubar. Los resultados demuestran que, aún existen madres que mantienen creencias, tabúes y mitos sobre la LM, debido a la desinformación y falta de contrastación de sus tradiciones. Se concluye que, la mayoría de las madres reproducen creencias, mitos o tabúes transmitidas por sus familiares de forma intergeneracional, siendo, por lo general, ideas erróneas y negativas sobre la LM

Derechos humanos e infancia: el rol del juego

Se presenta, en primer término, la temática de los valores en la vida humana, planteando definiciones y clasificaciones. Luego, se analiza el tema de los Derechos Humanos como un marco posible para extraer los valores. Posteriormente se aborda la Educación e ideas que conectan la educación con los DDHH. Se efectúa un análisis del juego y posibles definiciones, así como su clara conexión con el arte, ambas actividades humanas, en que lo lúdico y lo estético se manifiestan. Se analiza entonces, la conexión de estos elementos con el aspecto ético y por ende, con los DDHH. Se finaliza con un ejemplo de experiencia lúdico-estética y ética para niños y niñas