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Common Principal Components for Dependent Random Vectors

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  • Neuenschwander, Beat E.
  • Flury, Bernard D.

Abstract

Let the kp-variate random vector X be partitioned into k subvectors Xi of dimension p each, and let the covariance matrix [Psi] of X be partitioned analogously into submatrices [Psi]ij. The common principal component (CPC) model for dependent random vectors assumes the existence of an orthogonal p by p matrix [beta] such that [beta]t[Psi]ij[beta] is diagonal for all (i, j). After a formal definition of the model, normal theory maximum likelihood estimators are obtained. The asymptotic theory for the estimated orthogonal matrix is derived by a new technique of choosing proper subsets of functionally independent parameters.

Suggested Citation

  • Neuenschwander, Beat E. & Flury, Bernard D., 2000. "Common Principal Components for Dependent Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 163-183, November.
    • Handle: RePEc:eee:jmvana:v:75:y:2000:i:2:p:163-183
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    References listed on IDEAS

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    1. Flury, Bernhard W. & Schmid, Martin J., 1992. "Quadratic discriminant functions with constraints on the covariance matrices: Some asymptotic results," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 244-261, February.
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    Cited by:

    1. Fei Gu & Hao Wu, 2016. "Raw Data Maximum Likelihood Estimation for Common Principal Component Models: A State Space Approach," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 751-773, September.
    2. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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