Robust Identification of Subgraphs in a Complete Weighted Graph Associated with a Set of Random Variables

A class of distribution free multiple decision statistical procedures is proposed for threshold graph identification in a complete weighted graph associated with a set of random variables (random variables network). The decision procedures are based on simultaneous application of sign statistics. It is proved that single step, step down Holm and step up Hochberg statistical procedures for threshold graph identification are distribution free in sign similarity network in the class of elliptically contoured distributions.