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## RISK FUNCTION AND OPTIMALITY OF STATISTICAL PROCEDURES FOR IDENTIFICATION OF NETWORK STRUCTURES

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.