Testing linear independence in linear models with interval-valued data

Authors:
María Ángeles Gil;Gil González-Rodríguez;Ana Colubi;Manuel Montenegro
Affiliations:
Departamento de Estadística, I.O. y D.M., Universidad de Oviedo, C/Calvo Sotelo, s/n, 33007, 33071 Oviedo, Spain;Departamento de Estadística, I.O. y D.M., Universidad de Oviedo, C/Calvo Sotelo, s/n, 33007, 33071 Oviedo, Spain;Departamento de Estadística, I.O. y D.M., Universidad de Oviedo, C/Calvo Sotelo, s/n, 33007, 33071 Oviedo, Spain;Departamento de Estadística, I.O. y D.M., Universidad de Oviedo, C/Calvo Sotelo, s/n, 33007, 33071 Oviedo, Spain
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

Testing methods are introduced in order to determine whether there is some 'linear' relationship between imprecise predictor and response variables in a regression analysis. The variables are assumed to be interval-valued. Within this context, the variables are formalized as compact convex random sets, and an interval arithmetic-based linear model is considered. Then, a suitable equivalence for the hypothesis of linear independence in this model is obtained in terms of the mid-spread representations of the interval-valued variables. That is, in terms of some moments of random variables. Methods are constructed to test this equivalent hypothesis; in particular, the one based on bootstrap techniques will be applicable in a wide setting. The methodology is illustrated by means of a real-life example, and some simulation studies are considered to compare techniques in this framework.