Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 2 , pp. 195--200

AN INVARIANCE PRINCIPLE FOR $U$-STATISTICS WITH THE DEGREE OF THE KERNEL DEPENDING UPON THE SAMPLE SIZE

By

CHANDRAKANT M. DEO, University of Ottawa

SUMMARY. We prove an invariance principle for $U$-statistics where the degree of the kernel is allowed to depend upon the sample size. As an immediate consequence, we obtain a functional from of a recent theorem by van Es and Helmers (1988).

AMS (1990) subject classification. 60F,62G.

Key words and phrases. Invariance principles, $U$-statistics, symmetric statistics.

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