Abstract
Least-squares estimation of various linear models for interval data has already been considered in the literature. One of these models allows different slopes for mid-points and spreads (or radii) integrated in a unique equation based on interval arithmetic. A preliminary study about the construction of confidence regions for the parameters of that model on the basis of the least-squares estimators is presented. Due to the lack of realistic parametric models for random intervals, bootstrap approaches are proposed. The empirical suitability of the bootstrap confidence sets will be shown by means of some simulation studies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aumann, R.J.: Integrals of set-valued functions. J. Math. Anal. Appl. 12, 1–12 (1965)
Blanco-Fernández, A., Colubi, A., Corral, N., González-Rodríguez, G.: On a linear independence test for interval-valued random sets. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol. 48, pp. 331–337. Springer, Heidelberg (2008)
Blanco-Fernández, A., Corral, N., González-Rodríguez, G.: Estimation of a flexible simple linear model for interval data based on the set arithmetic (submitted for publication, 2010)
Gil, M.A., Lubiano, M.A., Montenegro, M., López-García, M.T.: Least squares fitting of an affine function and strength of association for interval-valued data. Metrika 56, 97–111 (2002)
Gil, M.A., González-Rodríguez, G., Colubi, A., Montenegro, M.: Testing linear independence in linear models with interval-valued data. Comput. Statist. Data Anal. 51(6), 3002–3015 (2007)
González-Rodríguez, G., Blanco-Fernández, A., Corral, N., Colubi, A.: Least squares estimation of linear regression models for convex compact random sets. Adv. Data Anal. Class. 1, 67–81 (2007)
Montenegro, M., Casals, M.R., Lubiano, M.A., Gil, M.A.: Two-sample hypothesis tests of means of a fuzzy random variable. Inf. Sci. 133, 89–100 (2001)
Montenegro, M., Colubi, A., Casals, M.R., Gil, M.A.: Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable. Metrika 59(1), 31–49 (2004)
Shao, J., Tu, D.: The Jackknife and Bootstrap. Springer, New York (1995)
Trutschnig, W., González-Rodríguez, G., Colubi, A., Gil, M.A.: A new family of metrics for compact convex (fuzzy) sets based on a generalized concept of mid and spread. Inf. Sci. 179(23), 3964–3972 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blanco-Fernández, A., Corral, N., González-Rodríguez, G., Palacio, A. (2010). On Some Confidence Regions to Estimate a Linear Regression Model for Interval Data. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-14746-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14745-6
Online ISBN: 978-3-642-14746-3
eBook Packages: EngineeringEngineering (R0)