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A new statistical depth function with applications to multimodal data

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  • W. Lok
  • Stephen Lee

Abstract

We propose a new statistical depth function based on interpoint distances, which has the distinct property of respecting multimodality in data configurations. This property proves to be especially relevant to many inference problems including confidence region construction, classification, tests for equality of populations, p-value computation, etc. With specification of an appropriate interpoint distance, our depth function also applies to infinite-dimensional data. A number of examples are used to illustrate the diverse applicability of our proposed depth function in different problem settings, where the conventional centre-outward ordering depth functions are found to be inadequate.

Suggested Citation

  • W. Lok & Stephen Lee, 2011. "A new statistical depth function with applications to multimodal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 617-631.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:617-631
    DOI: 10.1080/10485252.2011.553953
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    References listed on IDEAS

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    1. Paul R. Rosenbaum, 2005. "An exact distribution‐free test comparing two multivariate distributions based on adjacency," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 515-530, September.
    2. Lopez-Pintado, Sara & Romo, Juan, 2007. "Depth-based inference for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4957-4968, June.
    3. 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.
    4. Ricardo Fraiman & Jean Meloche & Luis García-Escudero & Alfonso Gordaliza & Xuming He & Ricardo Maronna & Víctor Yohai & Simon Sheather & Joseph McKean & Christopher Small & Andrew Wood & R. Fraiman &, 1999. "Multivariate L-estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 255-317, December.
    5. Peter Hall, 2002. "Permutation tests for equality of distributions in high-dimensional settings," Biometrika, Biometrika Trust, vol. 89(2), pages 359-374, June.
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    Cited by:

    1. Reza Modarres & Yu Song, 2020. "Multivariate power series interpoint distances," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 955-982, December.
    2. Kevin Leckey & Dennis Malcherczyk & Melanie Horn & Christine H. Müller, 2023. "Simple powerful robust tests based on sign depth," Statistical Papers, Springer, vol. 64(3), pages 857-882, June.

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