Moderate and large deviations for U-processes

Peter Eichelsbacher

Stochastic Processes and their Applications, 1998, vol. 74, issue 2, 273-296

Abstract: Sufficient conditions for the moderate and large deviation principle for U-processes are given. For the large deviation result the conditions are in terms of "blockwise" empirical process conditions. On the moderate scaling the case of U-processes indexed by a uniformly bounded VC subgraph class of functions is considered. The proofs are based on an isoperimetric inequality for empirical processes due to Talagrand, a truncation method based on an isoperimetric inequality by Ledoux, the existence of almost regular partitions of complete hypergraphs due to Baranyai and a Bernstein-type inequality for U-processes due to Arcones and Giné.

Keywords: Large; deviations; Moderate; deviations; U-statistics; U-processes; Isoperimetric; inequality; VC; classes; Bernstein's; inequality (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (1)

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