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Diffusions of perturbed principal component analysis

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  • Bru, Marie-France

Abstract

We propose a stochastic differential equation approach to principal component analysis. We give the equations governing the spectrum of the square BTB of a n-p matrix of independent Brownian motions. We apply this result to P.C.A. of perturbed continuous data.

Suggested Citation

  • Bru, Marie-France, 1989. "Diffusions of perturbed principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 127-136, April.
    • Handle: RePEc:eee:jmvana:v:29:y:1989:i:1:p:127-136
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    Cited by:

    1. Nourdin, Ivan & Pu, Fei, 2022. "Gaussian fluctuation for Gaussian Wishart matrices of overall correlation," Statistics & Probability Letters, Elsevier, vol. 181(C).
    2. Benjamin Jourdain & Ezéchiel Kahn, 2022. "Strong Solutions to a Beta-Wishart Particle System," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1574-1613, September.
    3. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    5. Stephan Lawi, 2008. "Towards a Characterization of Markov Processes Enjoying the Time-Inversion Property," Journal of Theoretical Probability, Springer, vol. 21(1), pages 144-168, March.
    6. Trinh, Hoang Dung & Trinh, Khanh Duy, 2021. "Beta Laguerre processes in a high temperature regime," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 192-205.
    7. Nualart, David & Pérez-Abreu, Victor, 2014. "On the eigenvalue process of a matrix fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4266-4282.
    8. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    9. Carlos G. Pacheco, 2016. "Picard Iterations for Diffusions on Symmetric Matrices," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1444-1457, December.
    10. Mayerhofer, Eberhard & Pfaffel, Oliver & Stelzer, Robert, 2011. "On strong solutions for positive definite jump diffusions," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2072-2086, September.
    11. Song, Jian & Yao, Jianfeng & Yuan, Wangjun, 2022. "Recent advances on eigenvalues of matrix-valued stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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