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Equivalency between vertices and centers-coupled-with-radii principal component analyses for interval data

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  • Hao, Chengcheng
  • Liang, Yuli
  • Roy, Anuradha

Abstract

Centers and vertices principal component analyses are common methods to explain variations within multivariate interval data. We introduce multivariate equicorrelated structures to vertices’ covariance. Assuming the structure, we show equivalence between centers and vertices methods by proving their eigensystems proportional.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:113-120
    DOI: 10.1016/j.spl.2015.07.005
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    References listed on IDEAS

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    1. Anuradha Roy, 2014. "A two-stage principal component analysis of symbolic data using equicorrelated and jointly equicorrelated covariance structures," Working Papers 0164mss, College of Business, University of Texas at San Antonio.
    2. 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.
    3. Giordani, Paolo & Kiers, Henk A.L., 2006. "A comparison of three methods for principal component analysis of fuzzy interval data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 379-397, November.
    4. Leiva, Ricardo, 2007. "Linear discrimination with equicorrelated training vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 384-409, February.
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    Cited by:

    1. 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.
    2. 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.

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