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Linear discrimination with equicorrelated training vectors

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  • Leiva, Ricardo

Abstract

Fisher's linear discrimination rule requires uncorrelated training vectors. In this paper a linear discrimination method is developed to be used when the training vectors are equicorrelated. Also, maximum likelihood ratio tests are proposed to decide whether the training samples are uncorrelated or equicorrelated.

Suggested Citation

  • Leiva, Ricardo, 2007. "Linear discrimination with equicorrelated training vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 384-409, February.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:2:p:384-409
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    References listed on IDEAS

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    1. 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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    Citations

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    Cited by:

    1. Anuradha Roy & Ricardo Leiva, 2013. "Testing the Equality of Mean Vectors for Paired Doubly Multivariate Observations," Working Papers 0180mss, College of Business, University of Texas at San Antonio.
    2. 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.
    3. 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.
    4. 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.
    5. Timothy Opheim & Anuradha Roy, 2021. "Linear models for multivariate repeated measures data with block exchangeable covariance structure," Computational Statistics, Springer, vol. 36(3), pages 1931-1963, September.
    6. Katarzyna Filipiak & Mateusz John & Daniel Klein, 2023. "Testing independence under a block compound symmetry covariance structure," Statistical Papers, Springer, vol. 64(2), pages 677-704, April.
    7. 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.
    8. Roy, Anuradha & Zmyślony, Roman & Fonseca, Miguel & Leiva, Ricardo, 2016. "Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 81-90.
    9. Pamela C. Smith & Dana A. Forgione, 2008. "Global Outsourcing of Healthcare: A Medical Tourism Decision Model," Working Papers 0033, College of Business, University of Texas at San Antonio.
    10. Hao, Chengcheng & Liang, Yuli & Roy, Anuradha, 2015. "Equivalency between vertices and centers-coupled-with-radii principal component analyses for interval data," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 113-120.
    11. Siyun Yang & Mirjam Moerbeek & Monica Taljaard & Fan Li, 2023. "Power analysis for cluster randomized trials with continuous coprimary endpoints," Biometrics, The International Biometric Society, vol. 79(2), pages 1293-1305, June.
    12. Anuradha Roy & Ricardo Leiva, 2008. "An Extension of the Traditional Classi cation Rules: the Case of Non-Random Samples," Working Papers 0057, College of Business, University of Texas at San Antonio.
    13. Anuradha Roy, 2010. "Linear Models for Multivariate Repeated Measures Data," Working Papers 0017, College of Business, University of Texas at San Antonio.
    14. Anuradha Roy & Ricardo Leiva, 2008. "Testing of a Structures Covariance Matrix for Three-Level Repeated Measures Data," Working Papers 0037, College of Business, University of Texas at San Antonio.
    15. Kihoon Yoon & Daijin Ko & Carolina B. Livi & Nathan Trinklein & Mark Doderer & Stephen Kwek & Luiz O. F. Penalva, 2008. "Over-represented sequences located on UTRs are potentially involved in regulatory functions," Working Papers 0053, College of Business, University of Texas at San Antonio.
    16. 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.
    17. Roy, Anuradha & Leiva, Ricardo, 2008. "Likelihood ratio tests for triply multivariate data with structured correlation on spatial repeated measurements," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1971-1980, September.

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    1. 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.
    2. 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.

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