Abstract:
Problems of network structures identification by sample of fixed size are considered. The concepts of random variables network and network model as complete weighted graph are introduced. Two types of network structures are introduced: network structures with fixed and arbitrary numbers of network model elements. Problems of network structures identification as multiple decision problems are considered. It is proved that risk functions of statistical procedures for network structures identification can be considered as linear combination of mean numbers of errors of incorrect inclusions and exclusions elements from network model to network structure.
Keywords:
random variables network, network model, network structure, identification procedure, first kind errors, second kind errors, additive loss, risk function.
Citation:
P. A. Koldanov, “Risk function of statistical procedures for network structures identification”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2017, no. 3, 45–59
\Bibitem{Kol17}
\by P.~A.~Koldanov
\paper Risk function of statistical procedures for network structures identification
\jour Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]
\yr 2017
\issue 3
\pages 45--59
\mathnet{http://mi.mathnet.ru/vtpmk178}
\crossref{https://doi.org/10.26456/vtpmk178}
Linking options:
https://www.mathnet.ru/eng/vtpmk178
https://www.mathnet.ru/eng/vtpmk/y2017/i3/p45
This publication is cited in the following 2 articles:
P. A. Koldanov, “Risk function and optimality of statistical procedures for identification of network structures”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2018, 317–326
Petr A. Koldanov, Springer Proceedings in Mathematics & Statistics, 247, Computational Aspects and Applications in Large-Scale Networks, 2018, 289
Citation in format AMSBIB
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