Abstract
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.
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Blanco-Fernández, A., Colubi, A., González-Rodríguez, G. (2013). Linear Regression Analysis for Interval-valued Data Based on Set Arithmetic: A Review. In: Borgelt, C., Gil, M., Sousa, J., Verleysen, M. (eds) Towards Advanced Data Analysis by Combining Soft Computing and Statistics. Studies in Fuzziness and Soft Computing, vol 285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30278-7_2
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DOI: https://doi.org/10.1007/978-3-642-30278-7_2
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