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Nonparametric statistics of dynamic networks with distinguishable nodes

Author

Listed:
  • Daniel Fraiman

    (Universidad de San Andrés
    Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET))

  • Nicolas Fraiman

    (University of North Carolina)

  • Ricardo Fraiman

    (Universidad de la República)

Abstract

The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, techniques for the statistical analysis of sequences of networks were less developed. In this paper, we focus on networks sequences with a fixed number of labeled nodes and study some statistical problems in a nonparametric framework. We introduce natural notions of center and a depth function for networks that evolve in time. We develop several statistical techniques including testing, supervised and unsupervised classification, and some notions of principal component sets in the space of networks. Some examples and asymptotic results are given, as well as two real data examples.

Suggested Citation

  • Daniel Fraiman & Nicolas Fraiman & Ricardo Fraiman, 2017. "Nonparametric statistics of dynamic networks with distinguishable nodes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 546-573, September.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0524-8
    DOI: 10.1007/s11749-017-0524-8
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    References listed on IDEAS

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    1. Miguel Arcones & Hengjian Cui & Yijun Zuo, 2006. "Empirical depth processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 151-177, June.
    2. G. Bonanno & G. Caldarelli & F. Lillo & S. Micciché & N. Vandewalle & R. Mantegna, 2004. "Networks of equities in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 38(2), pages 363-371, March.
    3. Diego Aparicio & Daniel Fraiman, 2015. "Banking Networks And Leverage Dependence In Emerging Countries," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 18(07n08), pages 1-21, November.
    4. D. Fraiman, 2008. "Growing directed networks: stationary in-degree probability for arbitrary out-degree one," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(3), pages 377-388, February.
    5. Dehling, Herold & Wendler, Martin, 2010. "Central limit theorem and the bootstrap for U-statistics of strongly mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 126-137, January.
    6. Petter Holme, 2015. "Modern temporal network theory: a colloquium," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(9), pages 1-30, September.
    7. Luca Greco & Alessio Farcomeni, 2016. "A plug-in approach to sparse and robust principal component analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 449-481, September.
    8. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The Tukey and the random Tukey depths characterize discrete distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2304-2311, November.
    9. Diego Aparicio & Daniel Fraiman, 2015. "Banking Networks and Leverage Dependence: Evidence from Selected Emerging Countries," Papers 1507.01901, arXiv.org.
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    Cited by:

    1. Zhang, Xu & Tian, Yahui & Guan, Guoyu & Gel, Yulia R., 2021. "Depth-based classification for relational data with multiple attributes," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    2. Agustín Alvarez & Marcela Svarc, 2021. "A variable selection procedure for depth measures," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 247-271, June.

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