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In search of non-Gaussian components of a high-dimensional distribution

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  • Blanchard, Gilles
  • Kawanabe, Motoaki
  • Sugiyama, Masashi
  • Spokoiny, Vladimir
  • Müller, Klaus-Robert

Abstract

Finding non-Gaussian components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the non-Gaussian subspace within a very general semi-parametric framework. Our proposed method, called NGCA (Non-Gaussian Component Analysis), is essentially based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector which belongs to the low dimensional non-Gaussian target subspace up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method.

Suggested Citation

  • Blanchard, Gilles & Kawanabe, Motoaki & Sugiyama, Masashi & Spokoiny, Vladimir & Müller, Klaus-Robert, 2006. "In search of non-Gaussian components of a high-dimensional distribution," SFB 649 Discussion Papers 2006-040, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  • Handle: RePEc:zbw:sfb649:sfb649dp2006-040
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    References listed on IDEAS

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    1. Trevor Cox, 2001. "Multidimensional scaling used in multivariate statistical process control," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(3-4), pages 365-378.
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    Cited by:

    1. Gutch, Harold W. & Theis, Fabian J., 2012. "Uniqueness of linear factorizations into independent subspaces," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 48-62.
    2. Panov, Vladimir, 2010. "Estimation of the signal subspace without estimation of the inverse covariance matrix," SFB 649 Discussion Papers 2010-050, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Diederichs, Elmar & Juditsky, Anatoli & Nemirovski, Arkadi & Spokoiny, Vladimir, 2011. "Sparse non Gaussian component analysis by semidefinite programming," SFB 649 Discussion Papers 2011-080, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Panov, Vladimir, 2010. "Non-gaussian component analysis: New ideas, new proofs, new applications," SFB 649 Discussion Papers 2010-026, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. repec:hum:wpaper:sfb649dp2011-080 is not listed on IDEAS

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