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Linear regression analysis for interval-valued data based on set arithmetic: a review. (English) Zbl 1348.62191

Borgelt, Christian (ed.) et al., Towards advanced data analysis by combining soft computing and statistics. Berlin: Springer (ISBN 978-3-642-30277-0/hbk; 978-3-642-30278-7/ebook). Studies in Fuzziness and Soft Computing 285, 19-31 (2013).
Summary: 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.
For the entire collection see [Zbl 1254.68014].

MSC:

62J05 Linear regression; mixed models
62J86 Fuzziness, and linear inference and regression
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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