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April, 1993 Wald's Equation for a Class of Denormalized $U$-Statistics
Y. S. Chow, V. H. de la Pena, H. Teicher
Ann. Probab. 21(2): 1151-1158 (April, 1993). DOI: 10.1214/aop/1176989285


Under suitable conditions on a stopping time $T$ and zero mean i.i.d. random variables $\{X_n, n \geq 1\}$, a Wald-type equation $ES_{k, T} = 0$ is obtained where $S_{k, n}$ is the sum of products of $k$ of the $X$'s with indices from 1 to $n$. This, in turn, is utilized to obtain information about the moments of $T_k = \inf\{n \geq k: S_{k, n} \geq 0\}$ and $W_c = \inf\{n \geq 2: S^2_{1, n} > c\sum^n_{j = 1}X^2_j\}, c > 0$.


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Y. S. Chow. V. H. de la Pena. H. Teicher. "Wald's Equation for a Class of Denormalized $U$-Statistics." Ann. Probab. 21 (2) 1151 - 1158, April, 1993.


Published: April, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0784.60039
MathSciNet: MR1217583
Digital Object Identifier: 10.1214/aop/1176989285

Primary: 60F99

Keywords: martingale inequalities , stopping times , Wald's equation

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 2 • April, 1993
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