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.

Full paper (PDF)