Linear regression model with histogram-valued variables

• Autor(a) principal: Sónia Dias
• Data de Publicação: 2015
• Outros Autores: Paula Brito
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://repositorio.inesctec.pt/handle/123456789/4586; http://dx.doi.org/10.1002/sam.11260

Histogram-valued variables are a particular kind of variables studied in Symbolic Data Analysis where to each entity under analysis corresponds a distribution that may be represented by a histogram or by a quantile function. Linear regression models for this type of data are necessarily more complex than a simple generalization of the classical model: the parameters cannot be negative; still the linear relation between the variables must be allowed to be either direct or inverse. In this work, we propose a new linear regression model for histogram-valued variables that solves this problem, named Distribution and Symmetric Distribution Regression Model. To determine the parameters of this model, it is necessary to solve a quadratic optimization problem, subject to non-negativity constraints on the unknowns; the error measure between the predicted and observed distributions uses the Mallows distance. As in classical analysis, the model is associated with a goodness-of-fit measure whose values range between 0 and 1. Using the proposed model, applications with real and simulated data are presented. © 2015 Wiley Periodicals, Inc.