Robust identification in random variable networks

•Robust statistical procedures for threshold graph identification are proposed.•Statistical procedures are based on simultaneous application of sign tests.•It is proved that well known multiple testing statistical procedures are robust.

A class of distribution free multiple decision statistical procedures is proposed for threshold graph identification in correlation networks. 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. Moreover it is shown that these procedures can be adapted for distribution free threshold graph identification in Pearson correlation network.