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Linear discrimination for three-level multivariate data with a separable additive mean vector and a doubly exchangeable covariance structure

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  • Leiva, Ricardo
  • Roy, Anuradha

Abstract

In this article, we study a new linear discriminant function for three-level m-variate observations under the assumption of multivariate normality. We assume that the m-variate observations have a doubly exchangeable covariance structure consisting of three unstructured covariance matrices for three multivariate levels and a separable additive structure on the mean vector. The new discriminant function is very efficient in discriminating individuals in a small sample scenario. An iterative algorithm is proposed to calculate the maximum likelihood estimates of the unknown population parameters as closed form solutions do not exist for these unknown parameters. The new discriminant function is applied to a real data set as well as to simulated data sets. We compare our findings with other linear discriminant functions for three-level multivariate data as well as with the traditional linear discriminant function.

Suggested Citation

  • Leiva, Ricardo & Roy, Anuradha, 2012. "Linear discrimination for three-level multivariate data with a separable additive mean vector and a doubly exchangeable covariance structure," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1644-1661.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1644-1661
    DOI: 10.1016/j.csda.2011.10.007
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    References listed on IDEAS

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    1. J. K. Lindsey, 1999. "Multivariate Elliptically Contoured Distributions for Repeated Measurements," Biometrics, The International Biometric Society, vol. 55(4), pages 1277-1280, December.
    2. Leiva, Ricardo, 2007. "Linear discrimination with equicorrelated training vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 384-409, February.
    3. Paranjpe, S. A. & Gore, A. P., 1994. "Selecting variables for discrimination when covariance matrices are unequal," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 417-419, December.
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    Cited by:

    1. Amitrajeet A. Batabyal & Hamid Beladi, 2015. "Optimal Transport Provision To A Tourist Destination: A Mechanism Design Approach," Working Papers 0140eco, College of Business, University of Texas at San Antonio.
    2. Arkadiusz Koziol & Anuradha Roy & Roman Zmyslony & Ricardo Leiva & Miguel Fonseca, 2016. "Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure," Working Papers 0149mss, College of Business, University of Texas at San Antonio.
    3. Ricardo Leiva & Anuradha Roy, 2016. "Multi-level multivariate normal distribution with self-similar compound symmetry covariance matrix," Working Papers 0146mss, College of Business, University of Texas at San Antonio.
    4. Roy, Anuradha & Leiva, Ricardo & Žežula, Ivan & Klein, Daniel, 2015. "Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 50-60.
    5. Tatjana Pavlenko & Anuradha Roy, 2013. "Supervised classifiers of ultra high-dimensional higher-order data with locally doubly exchangeable covariance structure," Working Papers 0185mss, College of Business, University of Texas at San Antonio.
    6. Carlos A. Coelho & Anuradha Roy, 2014. "Testing the hypothesis of a doubly exchangeable covariance matrix for elliptically contoured distributions," Working Papers 0145mss, College of Business, University of Texas at San Antonio.

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