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Optimizing Allocation Rules in Discrete and Continuous Discriminant Analysis

Author

Listed:
  • Dário Ferreira

    (Department of Mathematics, Center of Mathematics, University of Beira Interior, 6201-001 Covilhã, Portugal)

  • Sandra S. Ferreira

    (Department of Mathematics, Center of Mathematics, University of Beira Interior, 6201-001 Covilhã, Portugal)

Abstract

This paper presents an approach for the study of probabilistic outcomes in experiments with multiple possible results. An approach to obtain confidence ellipsoids for the vector of probabilities, which represents the likelihood of specific results, for both discrete and continuous discriminant analysis, is presented. The obtention of optimal allocation rules, in order to reduce the allocation costs is investigated. In the context of discrete discriminant analysis, the approach focuses on assigning elements to specific groups in an optimal way. Whereas in the continuous case, the approach involves determining the regions where each action is the optimal choice. The effectiveness of the proposed approach is examined with two numerical applications. One of them uses real data, while the other one uses simulated data.

Suggested Citation

  • Dário Ferreira & Sandra S. Ferreira, 2024. "Optimizing Allocation Rules in Discrete and Continuous Discriminant Analysis," Mathematics, MDPI, vol. 12(8), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1173-:d:1375280
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    References listed on IDEAS

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    1. McFarland, H. Richard & Richards, Donald St. P., 2001. "Exact Misclassification Probabilities for Plug-In Normal Quadratic Discriminant Functions. I. The Equal-Means Case," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 21-53, April.
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    1. McFarland, H. Richard & Richards, Donald St. P., 2002. "Exact Misclassification Probabilities for Plug-In Normal Quadratic Discriminant Functions: II. The Heterogeneous Case," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 299-330, August.

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