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Lorenz Model Selection

Author

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  • Paolo Giudici

    (University of Pavia)

  • Emanuela Raffinetti

    (University of Milan)

Abstract

In the paper, we introduce novel model selection measures based on Lorenz zonoids which, differently from measures based on correlations, are based on a mutual notion of variability and are more robust to the presence of outlying observations. By means of Lorenz zonoids, which in the univariate case correspond to the Gini coefficient, the contribution of each explanatory variable to the predictive power of a linear model can be measured more accurately. Exploiting Lorenz zonoids, we develop a Marginal Gini Contribution measure that allows to measure the absolute explanatory power of any covariate, and a Partial Gini Contribution measure that allows to measure the additional contribution of a new covariate to an existing model.

Suggested Citation

  • Paolo Giudici & Emanuela Raffinetti, 2020. "Lorenz Model Selection," Journal of Classification, Springer;The Classification Society, vol. 37(3), pages 754-768, October.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:3:d:10.1007_s00357-019-09358-w
    DOI: 10.1007/s00357-019-09358-w
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    References listed on IDEAS

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    1. Emanuela Raffinetti & Elena Siletti & Achille Vernizzi, 2015. "On the Gini coefficient normalization when attributes with negative values are considered," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 507-521, September.
    2. Giudici, Paolo & Abu-Hashish, Iman, 2019. "What determines bitcoin exchange prices? A network VAR approach," Finance Research Letters, Elsevier, vol. 28(C), pages 309-318.
    3. Gleb A. Koshevoy & Karl Mosler, 2007. "Multivariate Lorenz dominance based on zonoids," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 91(1), pages 57-76, March.
    4. David J. Hand & Heikki Mannila & Padhraic Smyth, 2001. "Principles of Data Mining," MIT Press Books, The MIT Press, edition 1, volume 1, number 026208290x, April.
    5. S Figini & P Giudici, 2011. "Statistical merging of rating models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(6), pages 1067-1074, June.
    6. Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
    7. Giudici, P. & Raffinetti, E., 2011. "On the Gini measure decomposition," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 133-139, January.
    8. Marco Dall’Aglio & Marco Scarsini, 2000. "Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex," ICER Working Papers - Applied Mathematics Series 27-2003, ICER - International Centre for Economic Research, revised Jul 2003.
    9. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    10. Raffaella Calabrese & Paolo Giudici, 2015. "Estimating bank default with generalised extreme value regression models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(11), pages 1783-1792, November.
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    Cited by:

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    2. Giudici, Paolo & Gramegna, Alex & Raffinetti, Emanuela, 2023. "Machine Learning Classification Model Comparison," Socio-Economic Planning Sciences, Elsevier, vol. 87(PB).
    3. Babaei, Golnoosh & Giudici, Paolo & Raffinetti, Emanuela, 2022. "Explainable artificial intelligence for crypto asset allocation," Finance Research Letters, Elsevier, vol. 47(PB).

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