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A multiple linear regression model for imprecise information

Author

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  • Maria Ferraro

    ()

  • Paolo Giordani

Abstract

In standard regression analysis the relationship between the (response) variable and a set of (explanatory) variables is investigated. In the classical framework the response is affected by probabilistic uncertainty (randomness) and, thus, treated as a random variable. However, the data can also be subjected to other kinds of uncertainty such as imprecision. A possible way to manage all of these uncertainties is represented by the concept of fuzzy random variable (FRV). The most common class of FRVs is the LR family (LR FRV), which allows us to express every FRV in terms of three random variables, namely, the center, the left spread and the right spread. In this work, limiting our attention to the LR FRV class, we consider the linear regression problem in the presence of one or more imprecise random elements. The procedure for estimating the model parameters and the determination coefficient are discussed and the hypothesis testing problem is addressed following a bootstrap approach. Furthermore, in order to illustrate how the proposed model works in practice, the results of a real-life example are given together with a comparison with those obtained by applying classical regression analysis. Copyright Springer-Verlag 2012

Suggested Citation

  • Maria Ferraro & Paolo Giordani, 2012. "A multiple linear regression model for imprecise information," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1049-1068, November.
  • Handle: RePEc:spr:metrik:v:75:y:2012:i:8:p:1049-1068
    DOI: 10.1007/s00184-011-0367-3
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    References listed on IDEAS

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    1. Guo, Peijun & Tanaka, Hideo, 2006. "Dual models for possibilistic regression analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 253-266, November.
    2. Ana Ramos-Guajardo & Ana Colubi & Gil González-Rodríguez & María Gil, 2010. "One-sample tests for a generalized Fréchet variance of a fuzzy random variable," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 185-202, March.
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