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Generalized Gini linear and quadratic discriminant analyses

Author

Listed:
  • Charles Condevaux

    (UNIV. NIMES CHROME)

  • Stéphane Mussard

    (UNIV. NIMES CHROME, Nîmes
    Grédi University of Sherbrooke
    Liser)

  • Téa Ouraga

    (UNIV. NIMES CHROME)

  • Guillaume Zambrano

    (UNIV. NIMES CHROME)

Abstract

In this paper, a linear discriminant analysis (LDA) is performed in the Gini sense (GDA). Maximizing the generalized Gini gross between-group matrix allows the data to be projected onto discriminant axes. Different methods are investigated, the geometrical approach—based on a particular distance—and the probabilistic approach, which consists in employing the generalized Gini within-group matrix in order to compute the conditional probability of ranking observations in specific groups. Tests based on U-statistics are proposed in order to test for discriminant variables instead of using the well-known Student test that requires homoskedasticity. Monte Carlo simulations show the robustness and the superiority of the GDA on contaminated data compared with various linear classifiers such as logit, SVM and LDA.

Suggested Citation

  • Charles Condevaux & Stéphane Mussard & Téa Ouraga & Guillaume Zambrano, 2020. "Generalized Gini linear and quadratic discriminant analyses," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 219-236, August.
    • Handle: RePEc:spr:metron:v:78:y:2020:i:2:d:10.1007_s40300-020-00178-2
    DOI: 10.1007/s40300-020-00178-2
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    1. Vasile Preda & Luigi-Ionut Catana, 2021. "Tsallis Log-Scale-Location Models. Moments, Gini Index and Some Stochastic Orders," Mathematics, MDPI, vol. 9(11), pages 1-22, May.

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