Estimation of a flexible simple linear model for interval data based on set arithmetic

Authors:
Angela Blanco-Fernández;Norberto Corral;Gil González-Rodríguez
Affiliations:
Dpto. de Estadística, I.O y D.M., Oviedo University, C/ Calvo Sotelo s/n, Oviedo 33007, Spain;Dpto. de Estadística, I.O y D.M., Oviedo University, C/ Calvo Sotelo s/n, Oviedo 33007, Spain;European Centre for Soft Computing, C/ Gonzalo Gutiérrez Quirós s/n, Mieres-Asturias 33600, Spain
Venue:
Computational Statistics & Data Analysis
Year:
2011

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Abstract

The estimation of a simple linear regression model when both the independent and dependent variable are interval valued is addressed. The regression model is defined by using the interval arithmetic, it considers the possibility of interval-valued disturbances, and it is less restrictive than existing models. After the theoretical formalization, the least-squares (LS) estimation of the linear model with respect to a suitable distance in the space of intervals is developed. The LS approach leads to a constrained minimization problem that is solved analytically. The strong consistency of the obtained estimators is proven. The estimation procedure is reinforced by a real-life application and some simulation studies.