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Stepwise estimation of common principal components

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  • Trendafilov, Nickolay T.

Abstract

The standard common principal components (CPCs) may not always be useful for simultaneous dimensionality reduction in k groups. Moreover, the original FG algorithm finds the CPCs in arbitrary order, which does not reflect their importance with respect to the explained variance. A possible alternative is to find an approximate common subspace for all k groups. A new stepwise estimation procedure for obtaining CPCs is proposed, which imitates standard PCA. The stepwise CPCs facilitate simultaneous dimensionality reduction, as their variances are decreasing at least approximately in all k groups. Thus, they can be a better alternative for dimensionality reduction than the standard CPCs. The stepwise CPCs are found sequentially by a very simple algorithm, based on the well-known power method for a single covariance/correlation matrix. Numerical illustrations on well-known data are considered.

Suggested Citation

  • Trendafilov, Nickolay T., 2010. "Stepwise estimation of common principal components," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3446-3457, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3446-3457
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    References listed on IDEAS

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    1. Schyns, M. & Haesbroeck, G. & Critchley, F., 2010. "RelaxMCD: Smooth optimisation for the Minimum Covariance Determinant estimator," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 843-857, April.
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    5. Trendafilov, Nickolay T. & Jolliffe, Ian T., 2006. "Projected gradient approach to the numerical solution of the SCoTLASS," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 242-253, January.
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    4. 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.
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