Measures of uncertainty in market network analysis

Statistical uncertainty of different filtration techniques for market network analysis is studied. Two measures of statistical uncertainty are discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases the second measure is a particular case of the first one. Statistical uncertainty for some popular market network structures is analyzed. Results of numerical evaluation of statistical uncertainty for minimum spanning tree, market graph, maximum cliques and maximum independent sets are given. The most stable structures are derived.