Risk function and optimality of statistical procedures for identification of network structures
P.A. Koldanov
National Research University Higher School of Economics, Nizhny Novgorod, 603025 Russia
For citation: Koldanov P.A. Risk function and optimality of statistical procedures for identification of network structures. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 2, pp. 317–326.
Для цитирования: Koldanov P.A. Risk function and optimality of statistical procedures for identification of network structures // Учен. зап. Казан. ун-та. Сер. Физ.-матем. науки. – 2018. – Т. 160, кн. 2. – С. 317–326.
Abstract
Identification of network structures using the finite-size sample has been considered. The concepts of random variables network and network model, which is a complete weighted graph, have been introduced. Two types of network structures have been investigated: network structures with an arbitrary number of elements and network structures with a fixed number of elements of the network model. The problem of identification of network structures has been investigated as a multiple testing problem. The risk function of statistical procedures for identification of network structures can be represented as a linear combination of expected numbers of incorrectly included elements and incorrectly non-included elements. The sufficient conditions of optimality for statistical procedures for network structures identification with an arbitrary number of elements have been given. The concept of statistical uncertainty of statistical procedures for identification of network structures has been introduced.
Keywords: random variables network, network model, network structure, procedure for identification of network structure, additive loss function, risk function, unbiasedness, optimality, statistical uncertainty
Acknowledgments. This work was supported in part by the Laboratory of Algorithms and Technologies for Network Analysis of National Research University Higher School of Economics and by the Russian Foundation for Basic Research (project no. 18-07-00524).
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Recieved
October 10, 2017
Koldanov Petr Alexandrovich, Candidate of Technical Sciences
National Research University Higher School of Economics
ul. B. Pecherskaya 2, Nizhny Novgorod, 603025 Russia
E-mail: pkoldanov@hse.ru
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