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Generalization of the Mahalanobis Distance in the Mixed Case

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  • Barhen, A.
  • Daudin, J. J.

Abstract

The Mahalanobis distance is extended to the case where the variables are a mixture of discrete and continuous variables. The distributional properties are studied for the location model and asymptotical results are obtained for the general parametric case. The rate of convergence is evaluated through simulation. An example of these techniques is presented.

Suggested Citation

  • Barhen, A. & Daudin, J. J., 1995. "Generalization of the Mahalanobis Distance in the Mixed Case," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 332-342, May.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:2:p:332-342
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    Cited by:

    1. Cheng, Tsung-Chi & Biswas, Atanu, 2008. "Maximum trimmed likelihood estimator for multivariate mixed continuous and categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2042-2065, January.
    2. Alban Mbina Mbina & Guy Martial Nkiet & Fulgence Eyi Obiang, 2019. "Variable selection in discriminant analysis for mixed continuous-binary variables and several groups," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 773-795, September.
    3. de Leon, A.R. & Zhu, Y., 2008. "ANOVA extensions for mixed discrete and continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2218-2227, January.
    4. Mortier, F. & Robin, S. & Lassalvy, S. & Baril, C.P. & Bar-Hen, A., 2006. "Prediction of Euclidean distances with discrete and continuous outcomes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1799-1814, September.
    5. Merbouha, A. & Mkhadri, A., 2004. "Regularization of the location model in discrimination with mixed discrete and continuous variables," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 563-576, April.
    6. Daudin, J. J. & Bar-Hen, A., 1999. "Selection in discriminant analysis with continuous and discrete variables," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 161-175, December.
    7. de Leon, A. R. & Carrière, K. C., 2005. "A generalized Mahalanobis distance for mixed data," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 174-185, January.

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