Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 1, pp. 167--170

ON LARGE DEVIATIONS OF U-STATISTICS AND THEIR PROJECTIONS

By

L. BARINGHAUS, *Universität Hannover*

and

R. RANK, *Zütrich Rütckversicherung*

*SUMMARY. *The paper presents a simple example showing that, in general, large deviation
probabilities of *U*-statistics
and their projections behave in a different manner. This
disproves a theorem of Dasgupta which was used in the past
to obtain the Bahadur efficiency of statistical tests based on
*U*-statistics or *V*-statistics.

*AMS (1991) subject classification. *Primary 60F10; secondary 62F05.

*Key words and phrases. * *U*-statistics, projections, large deviations.