Linear Regression Analysis for Interval-valued Data Based on Set Arithmetic: A Review
When working with real-valued data regression analysis allows to model and forecast the values of a random variable in terms of the values of either another one or several other random variables defined on the same probability space. When data are not real-valued, regression techniques should be extended and adapted to model simply relationships in an effective way. Different kinds of imprecision may appear in experimental data: uncertainty in the quantification of the data, subjective measurements, perceptions, to name but a few. Compact intervals can be effectively used to represent these imprecise data. Set- and fuzzy-valued elements are also employed for representing different kinds of imprecise data. In this paper several linear regression estimation techniques for interval-valued data are revised. Both the practical applicability and the empirical behaviour of the estimation methods is studied by comparing the performance of the techniques under different population conditions.
KeywordsRegression Problem Interval Arithmetic Random Interval Fuzzy Random Variable Simple Linear Model
Unable to display preview. Download preview PDF.
- 6.González-Rodríguez, G., Colubi, A., Coppi, R., Giordani, P.: On the estimation of linear models with interval-valued data. In: Proc. 17th IASC. Physica-Verlag, Heidelberg (2006)Google Scholar
- 9.Körner, R., Näther, W.: On the variance of random fuzzy variables. In: Stat. Mod. Anal. Manag. Fuzzy D., pp. 22–39. Physica-Verlag, Heidelberg (2002)Google Scholar