Linear regression model with histogram‐valued variables. (22nd April 2015)

• Record Type: Journal Article
• Authors: Dias, Sónia; Brito, Paula
• Is Part Of: Statistical analysis and data mining. Volume 8:Number 2(2015)
• Page Start: 75
• Page End: 113
• Publication Date: 2015-04-22
• Subjects: Data mining -- Statistical methods -- Periodicals; 006.312
• DOI: 10.1002/sam.11260
• Languages: English
• ISSNs: 1932-1864

Abstract

<abstract abstract-type="main" id="sam11260-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="sam11260-para-0001">Histogram‐valued variables are a particular kind of variables studied in <italic>Symbolic Data Analysis</italic> 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 <italic>Distribution and Symmetric Distribution Regression Model</italic>. 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.</p> </abstract>