Moderate and large deviations for \(U\)-processes (Q1805756)

The author derives results on moderate and large deviations of \(U\)-processes related to a sequence of i.i.d. random variables. The conditions on the large deviation result are formulated in terms of blockwise empirical process conditions. The proofs are based on an isoperimetric inequality for empirical processes due to Talagrand, a truncation method based on isoperimetric inequality by Ledoux, the existence of almost sure regular partitions of complete hypergraphs due to Baranyai and a Bernstein-type inequality for \(U\)-processes due to Arcones and Giné.