Multivariate Analysis of Distributional Data

• Activity Number: 315
• Type: Invited
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Paula Brito*+
• Companies: FEP & LIAAD INESC TEC - UNIV.PORTO
• Keywords: complex data ; distribution data ; histogram-valued variables ; symbolic data

Abstract

In statistics and multivariate data analysis, the units under analysis are usually single elements described by numerical and/or categorical variables, each element taking one value for each variable. However, it often happens that the data under analysis are not single observations, but groups of units gathered on the basis of common properties, or observed repeatedly over time, or concepts described as such - therefore the observed values present variability. In such situations, data is usually reduced to central statistics leading to loss of important information. Symbolic Data Analysis provides a framework where the variability observed may effectively be considered in the data representation, and methods developed that take it into account. To describe groups of individuals or concepts, new variables types have been introduced, which may now assume other forms of realizations, taking into account the data intrinsic variability, these are now sets, intervals or distributions for each entity. In this talk, we focus on the case where individual observations are summarized by distributions, and recall some methods that have been developed to analyse such data.