Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 1, pp. 142--148

MOMENT INEQUALITIES FOR U-STATISTICS WITH DEGENERACY OF HIGHER ORDER

By

DIETMAR FERGER, University of Giessen

SUMMARY.  Let Un be a d-degenerate U-statistic of degree m pertaining to a sample of independent and identically distributed random variables. We provide a sharp upper bound for the r-th, $r \geq 1$ absolute central moment of Un . Besides the novelty of our result its proof involves an induction on the degree of degeneracy. This technique is new in the literature of U-statistics.

AMS (1980) subject classification.  Primary 60E15, 60G99, secondary 60G42.

Key words and phrases. Degenerate $U$-statistic, Hoeffding decomposition, upper moment bounds, martingales.

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