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Some hypothesis tests based on random projection

Author

Listed:
  • Ricardo Fraiman

    (Universidad de la República)

  • Leonardo Moreno

    (Universidad de la República)

  • Sebastian Vallejo

    (Grupo MAS)

Abstract

Two new non-parametric tests are proposed based on continuous one-dimensional random projections. The first one addresses central symmetry and the second addresses independence. These tests are implemented for finite and infinite dimensional (functional) data sets. Both tests are distribution-free and universally consistent. Additionally, different techniques are proposed to improve the power of the tests. Promising results have been obtained by comparing the new tests with existing ones using simulation study. Real data in Banach spaces have been used to develop an application.

Suggested Citation

  • Ricardo Fraiman & Leonardo Moreno & Sebastian Vallejo, 2017. "Some hypothesis tests based on random projection," Computational Statistics, Springer, vol. 32(3), pages 1165-1189, September.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-017-0732-4
    DOI: 10.1007/s00180-017-0732-4
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    References listed on IDEAS

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    5. Rainer Dyckerhoff & Christophe Ley & Davy Paindaveine, 2015. "Depth-based runs tests for bivariate central symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 917-941, October.
    6. Cuevas, Antonio & Fraiman, Ricardo, 2009. "On depth measures and dual statistics. A methodology for dealing with general data," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 753-766, April.
    7. David Blough, 1989. "Multivariate symmetry via projection pursuit," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 461-475, September.
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    Cited by:

    1. Yasser Al Zaim & Mohammad Reza Faridrohani, 2021. "Bayesian random projection-based signal detection for Gaussian scale space random fields," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 503-532, September.
    2. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.

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