Large Deviations of U-Statistics


Yuri V. Borovskikh and Neville C. Weber


Research Report 2001-1
Date: 12 January 2001


Large deviation results with explicit order terms and Cramer's series are developed for non-degenerate U-statistics of degree m under Cramer type conditions on the kernel. The method of the proof is based on the contraction technique of Keener, Robinson and Weber (1998), which is the natural generalization of the classical method of Cramer (1938). Other techniques used in the proofs include truncation, decoupling inequalities, Borell's inequality for Rademacher chaos and a partitioning method to bound the degenerate remainder term.

Key phrases

Large deviations. U-statistics. Cramer's series. Decoupling inequalities.

AMS Subject Classification (1991)

Primary: 60F10


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