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On the distribution of the left singular vectors of a random matrix and its applications

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  • Bura, E.
  • Pfeiffer, R.

Abstract

In several dimension reduction techniques, the original variables are replaced by a smaller number of linear combinations. The coefficients of these linear combinations are typically the elements of the left singular vectors of a random matrix. We derive the asymptotic distribution of the left singular vectors of a random matrix that has a normal limit distribution. This result is then used to develop a Wald-type test for testing variable importance in Sliced Inverse Regression (SIR) and Sliced Average Variance Estimation (SAVE), two popular sufficient dimension reduction methods.

Suggested Citation

  • Bura, E. & Pfeiffer, R., 2008. "On the distribution of the left singular vectors of a random matrix and its applications," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2275-2280, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2275-2280
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    References listed on IDEAS

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    1. Zaka Ratsimalahelo, 2003. "Rank Test Based On Matrix Perturbation Theory," Econometrics 0306008, University Library of Munich, Germany.
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    Cited by:

    1. Jang, Hyun Jung & Shin, Seung Jun & Artemiou, Andreas, 2023. "Principal weighted least square support vector machine: An online dimension-reduction tool for binary classification," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    2. repec:spo:wpecon:info:hdl:2441/7o52iohb7k6srk09n8t4k21sm is not listed on IDEAS
    3. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric spectral-based estimation of latent structures," CeMMAP working papers 18/14, Institute for Fiscal Studies.
    4. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," SciencePo Working papers hal-00972868, HAL.
    5. repec:spo:wpmain:info:hdl:2441/7o52iohb7k6srk09n8t4k21sm is not listed on IDEAS
    6. Seung Jun Shin & Yichao Wu & Hao Helen Zhang & Yufeng Liu, 2017. "Principal weighted support vector machines for sufficient dimension reduction in binary classification," Biometrika, Biometrika Trust, vol. 104(1), pages 67-81.
    7. repec:hal:wpspec:info:hdl:2441/7o52iohb7k6srk09n8t4k21sm is not listed on IDEAS
    8. repec:hal:spmain:info:hdl:2441/7o52iohb7k6srk09n8t4k21sm is not listed on IDEAS
    9. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric estimation of finite measures," CeMMAP working papers CWP11/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Jerome R. Simons, 2023. "Inference on eigenvectors of non-symmetric matrices," Papers 2303.18233, arXiv.org, revised Apr 2023.
    11. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 130-142, January.

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