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Prediction of Euclidean distances with discrete and continuous outcomes

Author

Listed:
  • Mortier, F.
  • Robin, S.
  • Lassalvy, S.
  • Baril, C.P.
  • Bar-Hen, A.

Abstract

The objective of this paper is first to predict generalized Euclidean distances in the context of discrete and quantitative variables and then to derive their statistical properties. We first consider the simultaneous modelling of discrete and continuous random variables with covariates and obtain the likelihood. We derive an important property useful for its practical maximization. We then study the prediction of any Euclidean distances and its statistical proprieties, especially for the Mahalanobis distance. The quality of distance estimation is analyzed through simulations. This results are applied to our motivating example: the official distinction procedure of rapeseed varieties.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1799-1814
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    References listed on IDEAS

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    1. 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.
    2. Wai-Yin Poon & Sik-Yum Lee, 1987. "Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 409-430, September.
    3. Edward J. Bedrick & Jodi Lapidus & Joseph F. Powell, 2000. "Estimating the Mahalanobis Distance from Mixed Continuous and Discrete Data," Biometrics, The International Biometric Society, vol. 56(2), pages 394-401, June.
    4. 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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    Cited by:

    1. Chaubert, F. & Mortier, F. & Saint André, L., 2008. "Multivariate dynamic model for ordinal outcomes," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1717-1732, September.
    2. Pierrette Chagneau & Frédéric Mortier & Nicolas Picard & Jean-Noël Bacro, 2011. "A Hierarchical Bayesian Model for Spatial Prediction of Multivariate Non-Gaussian Random Fields," Biometrics, The International Biometric Society, vol. 67(1), pages 97-105, March.

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