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A Minmax Regret Linear Regression Model Under Uncertainty in the Dependent Variable

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  • Eduardo Conde

    (University of Seville)

Abstract

This paper analyzes the simple linear regression model corresponding to a sample affected by errors from a non-probabilistic viewpoint. We consider the simplest case where the errors just affect the dependent variable and there only exists one explanatory variable. Moreover, we assume the errors affecting each observation can be bounded. In this context the minmax regret criterion is used in order to obtain a regression line with nearly optimal goodness of fit for any true values of the dependent variable. Theoretical results as well as numerical methods are stated in order to solve the optimization problem under different residual cost functions.

Suggested Citation

  • Eduardo Conde, 2014. "A Minmax Regret Linear Regression Model Under Uncertainty in the Dependent Variable," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 573-596, February.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:2:d:10.1007_s10957-013-0304-x
    DOI: 10.1007/s10957-013-0304-x
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    References listed on IDEAS

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    1. G. Yu, 1998. "Min-Max Optimization of Several Classical Discrete Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 221-242, July.
    2. Lee, Haekwan & Tanaka, Hideo, 1999. "Upper and lower approximation models in interval regression using regression quantile techniques," European Journal of Operational Research, Elsevier, vol. 116(3), pages 653-666, August.
    3. T. Assavapokee & M. J. Realff & J. C. Ammons, 2008. "Min-Max Regret Robust Optimization Approach on Interval Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 297-316, May.
    4. Tanaka, Hideo & Hayashi, Isao & Watada, Junzo, 1989. "Possibilistic linear regression analysis for fuzzy data," European Journal of Operational Research, Elsevier, vol. 40(3), pages 389-396, June.
    5. Hojati, Mehran & Bector, C. R. & Smimou, Kamal, 2005. "A simple method for computation of fuzzy linear regression," European Journal of Operational Research, Elsevier, vol. 166(1), pages 172-184, October.
    6. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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