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Some high-dimensional one-sample tests based on functions of interpoint distances

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  • Saha, Enakshi
  • Sarkar, Soham
  • Ghosh, Anil K.

Abstract

The multivariate one-sample location problem is well studied in the literature, and several tests are available for it. But most of the existing one-sample tests perform poorly for high-dimensional data, and many of them are not even applicable when the dimension of the data exceeds the sample size. In this article, we develop and investigate some nonparametric one-sample tests based on functions of interpoint distances. These proposed tests can be conveniently used in high dimension, low sample size (HDLSS) situations, and good power properties of these tests for HDLSS data have been established using theoretical as well as numerical results.

Suggested Citation

  • Saha, Enakshi & Sarkar, Soham & Ghosh, Anil K., 2017. "Some high-dimensional one-sample tests based on functions of interpoint distances," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 83-95.
    • Handle: RePEc:eee:jmvana:v:161:y:2017:i:c:p:83-95
    DOI: 10.1016/j.jmva.2017.07.006
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    References listed on IDEAS

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    1. Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444, June.
    2. Biswas, Munmun & Ghosh, Anil K., 2014. "A nonparametric two-sample test applicable to high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 160-171.
    3. Lan Wang & Bo Peng & Runze Li, 2015. "A High-Dimensional Nonparametric Multivariate Test for Mean Vector," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1658-1669, December.
    4. Srivastava, Muni S., 2009. "A test for the mean vector with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 518-532, March.
    5. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    6. Munmun Biswas & Minerva Mukhopadhyay & Anil K. Ghosh, 2014. "A distribution-free two-sample run test applicable to high-dimensional data," Biometrika, Biometrika Trust, vol. 101(4), pages 913-926.
    7. Jinyuan Chang & Chao Zheng & Wen‐Xin Zhou & Wen Zhou, 2017. "Simulation‐based hypothesis testing of high dimensional means under covariance heterogeneity," Biometrics, The International Biometric Society, vol. 73(4), pages 1300-1310, December.
    8. Denis Larocque & Serge Tardif & Constance van Eeden, 2000. "Bivariate Sign Tests Based on the Sup, L 1 and L 2 Norms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 488-506, September.
    9. Srivastava, Muni S. & Du, Meng, 2008. "A test for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 386-402, March.
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    Cited by:

    1. 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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