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.
Large deviations. U-statistics. Cramer's series. Decoupling inequalities.
AMS Subject Classification (1991)
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