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Non-Gaussian Component Analysis: Testing the Dimension of the Signal Subspace

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Analytical Methods in Statistics (AMISTAT 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 329))

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Abstract

Dimension reduction is a common strategy in multivariate data analysis which seeks a subspace which contains all interesting features needed for the subsequent analysis. Non-Gaussian component analysis attempts for this purpose to divide the data into a non-Gaussian part, the signal, and a Gaussian part, the noise. We will show that the simultaneous use of two scatter functionals can be used for this purpose and suggest a bootstrap test to test the dimension of the non-Gaussian subspace. Sequential application of the test can then for example be used to estimate the signal dimension.

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Acknowledgements

The authors wish to express their gratitude to two anonymous referees, whose insightful comments greatly helped improving the quality of the manuscript. The work of KN was supported by the Austrian Science Fund (FWF) Grant number P31881-N32.

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Authors and Affiliations

  1. Institute of Statistics & Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstr. 7, 1040, Vienna, Austria

    Una Radojičić & Klaus Nordhausen

Authors
  1. Una Radojičić
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  2. Klaus Nordhausen
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Corresponding author

Correspondence to Una Radojičić .

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Editors and Affiliations

  1. Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic

    Matúš Maciak

  2. Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic

    Michal Pešta

  3. Department of Applied Mathematics, Technical University of Liberec, Liberec, Czech Republic

    Martin Schindler

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Radojičić, U., Nordhausen, K. (2020). Non-Gaussian Component Analysis: Testing the Dimension of the Signal Subspace. In: Maciak, M., Pešta, M., Schindler, M. (eds) Analytical Methods in Statistics. AMISTAT 2019. Springer Proceedings in Mathematics & Statistics, vol 329. Springer, Cham. https://doi.org/10.1007/978-3-030-48814-7_6

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