Geodesic
Risk function and optimality of statistical procedures for identification of network structures
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 2, pp. 317-326 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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P. A. Koldanov. Risk function and optimality of statistical procedures for identification of network structures. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 2, pp. 317-326. http://geodesic.mathdoc.fr/item/UZKU_2018_160_2_a12/

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