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Monotonicity properties of spatial depth

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  • Nagy, Stanislav

Abstract

We investigate the monotonicity properties of the spatial depth for multivariate data. We show that the spatial depth does not decrease monotonically with respect to the deepest point. Moreover, an answer to the conjecture of Gao (2003) is provided.

Suggested Citation

  • Nagy, Stanislav, 2017. "Monotonicity properties of spatial depth," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 373-378.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:373-378
    DOI: 10.1016/j.spl.2017.06.025
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    References listed on IDEAS

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    1. Carlo Sguera & Pedro Galeano & Rosa Lillo, 2014. "Spatial depth-based classification for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 725-750, December.
    2. Gao, Yonghong, 2003. "Data depth based on spatial rank," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 217-225, November.
    3. Serfling, Robert & Wijesuriya, Uditha, 2017. "Depth-based nonparametric description of functional data, with emphasis on use of spatial depth," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 24-45.
    4. Jun Li & Xin Zhang & Daniel R. Jeske, 2013. "Nonparametric multivariate CUSUM control charts for location and scale changes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 1-20, March.
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