On Wald's equation for U-statistical sums


Yuri V. Borovskikh and Neville C. Weber


Research Report 98-25
Published in Statistics and Probability Letters 44 (1999)
Date: 12 January 2000


We obtain Wald's equation for de-normalized U-statistics of degree m in the spirit of similar recent results by de la Pena and Lai. The proof uses Young's inequalities to obtain alternate conditions under which Wald's equation holds.

Key phrases

Wald's equation. stopping times. U-statistics. martingale inequalities.

AMS Subject Classification (1991)

Primary: 60F99, 60G40