2013/03/25 by Sónia Dias, Dias, Sónia, Paula Brito +1
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #stat.ME
paper · pdf · doi:10.48550/arxiv.1303.6199
49 pages 17 figures
arxiv created 2013/03/25 · arxiv updated 2013/03/26
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 relationship 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.