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.