Invariance Properties of Statistical Procedures for Network Structures Identification

  • Petr A. KoldanovEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 247)


Invariance properties of statistical procedures for threshold graph identification are considered. An optimal procedure in the class of invariant multiple decision procedures is constructed.


Random variables network Network model Network structures Threshold graph Uniformly most powerful test Invariance Unbiasedness 



The work is partially supported by RFHR grant 15-32-01052 (Sections 3, 4) and RFFI grant 18-07-00524 (Section 5).


  1. 1.
    Anderson, T.W.: An Introduction to Multivariate Statistical Analysis, 3rd edn. Wiley-Interscience, New York (2003)Google Scholar
  2. 2.
    Boginski, V., Butenko, S., Pardalos, P.M.: On structural properties of the market graph. In: Nagurney, A. (ed.) Innovations in Financial and Economic Networks, pp. 29–45. Springer (2003)Google Scholar
  3. 3.
    Gather, U., Pawlitschko, J.: A note on invariance of multiple tests. Stat. Neerl. 51(3), 366–372 (1997)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Jordan, M.I.: Graphical models. Stat. Sci. 19, 140–155 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Kalyagin, V.A., Koldanov, A.P., Koldanov, P.A.: Robust identification in random variables networks. J. Stat. Plann. Inference 181, 30–40 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kalyagin, V.A., Koldanov, A.P., Koldanov, P.A., Pardalos, P.M.: Optimal decision for the market graph identification problem in a sign similarity network. Ann. Oper. Res. (2017).
  7. 7.
    Koldanov, P.A.: Risk function of statistical procedures for network structures identification. Vestnik TvGU. Seriya: Prikladnaya Matematika [Trudy of Tver State University. Series: Applied Mathematics], no. 3, pp. 45–59 (2017) (in Russian)Google Scholar
  8. 8.
    Koldanov, A.P., Kalyagin, V.A., Koldanov, P.A., Pardalos, P.M.: Statistical procedures for the market graph construction. Comput. Stat. Data Anal. 68, 17–29 (2013)Google Scholar
  9. 9.
    Lehmann, E.L.: A theory of some multiple decision problems. Ann. Math. Stat. 1–25 (1957)Google Scholar
  10. 10.
    Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses. Springer, New York (2005)zbMATHGoogle Scholar
  11. 11.
    Wald, A.: Statistical Decision Functions. Springer (1950)Google Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Algorithms and Technologies for Network AnalysisNational Research University Higher School of EconomicsNizhny NovgorodRussia

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