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An Exponential Inequality for U-Statistics with Applications to Testing*

Published online by Cambridge University Press:  27 July 2009

Peter J. Bickel  and
Ya'acov Ritov
Peter J. Bickel
Affiliation:
Department of Statistics, University of California, Berkeley, California 94720
Ya'acov Ritov
Affiliation:
Department of Statistics, The Hebrew University, 91905 Jerusalem, Israel
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Abstract

We present a new exponential inequality for degenerate U-statistics. The bound on the tail probability is quadratic for small to medium values of the deviation and linear for larger values. We apply this bound to a family of test statistics and provide the key step in an optimality result for adaptive tests [1].

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 1 , January 1995 , pp. 39 - 52
Copyright
Copyright © Cambridge University Press 1995

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References

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