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.