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Probability densities from distances and discrimination

Author

Listed:
  • Cuadras, C. M.
  • Atkinson, R. A.
  • Fortiana, J.

Abstract

Given a population and a random vector X, by using distances between observations of X, we prove that it is, in general, possible to construct probability densities for X. This distance-based approach can present problems, from a multidimensional scaling point of view, for some monotonic density functions, where the construction must be made on the basis of symmetric functions instead of distances. A measure of divergence between the true density and this construction is given. The procedure aims to offer alternative methods for performing discriminant analysis.

Suggested Citation

  • Cuadras, C. M. & Atkinson, R. A. & Fortiana, J., 1997. "Probability densities from distances and discrimination," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 405-411, May.
  • Handle: RePEc:eee:stapro:v:33:y:1997:i:4:p:405-411
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    References listed on IDEAS

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    1. Cuadras, C. M. & Fortiana, J., 1995. "A Continuous Metric Scaling Solution for a Random Variable," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 1-14, January.
    2. Cuadras, C. M., 1992. "Probability distributions with given multivariate marginals and given dependence structure," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 51-66, July.
    3. W. Krzanowski, 1994. "Ordination in the presence of group structure, for general multivariate data," Journal of Classification, Springer;The Classification Society, vol. 11(2), pages 195-207, September.
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