Neyman-Pearson(NP)　criterion　is　one　of　the　most　important　ways　in　hypothesis　testing.　It　is　also　a　criterion　for　classification.　This　paper　addresses　the　problem　of　bounding　the　estimation　error　of　NP　classification,　in　terms　of　Rademacher　averages.　We　investigate　the　behavior　of　the　global　and　local　Rademacher　averages,　and　present　new　NP　classification　error　bounds　which　are　based　on　the　localized　averages,　and　indicate　how　the　estimation　error　can　be　estimated　without　a　priori　knowledge　of　the　class　at　hand.