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August, 1970 Moment Inequalities for the Maximum Cumulative Sum
R. J. Serfling
Ann. Math. Statist. 41(4): 1227-1234 (August, 1970). DOI: 10.1214/aoms/1177696898


Assume $E(X_i) \equiv 0$. For $\nu \geqq 2$, bounds on the $\nu$th moment of $\max_{1 \leqq k \leqq n}|\sum^{a + k}_{a + 1} X_i|$ are deduced from assumed bounds on the $\nu$th moment of $|\sum^{a + n}_{a + 1} X_i|$. The inequality due to Rademacher-Mensov for $\nu = 2$ and orthogonal $X_i$'s is generalized to $\nu \geqq 2$ and other types of dependent $\operatorname{rv's}.$ In the case $\nu > 2$, a second result is obtained which is considerably stronger than the first for asymptotic applications.


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R. J. Serfling. "Moment Inequalities for the Maximum Cumulative Sum." Ann. Math. Statist. 41 (4) 1227 - 1234, August, 1970.


Published: August, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0272.60013
MathSciNet: MR268938
Digital Object Identifier: 10.1214/aoms/1177696898

Rights: Copyright © 1970 Institute of Mathematical Statistics

Vol.41 • No. 4 • August, 1970
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