Robust identification in random variable networks

• Published in: Journal of statistical planning and inference Vol. 181; pp. 30 - 40
• Main Authors: Kalyagin, Valery A., Koldanov, Alexander P., Koldanov, Petr A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2017
• Subjects: Correlation networks; Distribution free decision procedures; Elliptically contoured distributions; Hochberg procedure; Holm procedure; Multiple decision statistical procedures; Pearson correlation; Random variable networks; Risk function; Sign similarity; Threshold graph; 62H15; Threshold graph; Risk function; Correlation networks; Random variable networks; Elliptically contoured distributions; Hochberg procedure; Holm procedure; 90B15; Sign similarity; Multiple decision statistical procedures; 62H20; Distribution free decision procedures; Pearson correlation
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2016.08.008

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. •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.