Linear regression model with histogram-valued variables

• Type: Article in International Scientific Journal
• Date: 2015

Authors

S. Dias (Author) Other; P. Brito (Author) FEP

Journal

Title: Statistical Analysis and Data Mining

Vol. 8

Pages: 75-113

ISSN: 1932-1864

Publisher: Wiley-Blackwell

Indexing

ISI Web of Knowledge - 19 Citations

Scopus - 27 Citations

Scientific classification

FOS: Natural sciences > Mathematics

CORDIS: Physical sciences > Mathematics > Statistics

Other information

Authenticus ID: P-00A-CXF

DOI: 10.1002/sam.11260

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific