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October, 1972 Rates of Convergence for Weighted Sums of Random Variables
F. T. Wright
Ann. Math. Statist. 43(5): 1687-1691 (October, 1972). DOI: 10.1214/aoms/1177692403


For $N = 1,2,\cdots$ let $S_N = \sum_k a_{N,k}X_k$ where $a_{N,k}$ is a real number for $N,k = 1,2, \cdots$ and $\{Xk\}$ is a sequence of not necessarily independent random variables. For the case $0 < t < 1$, with assumptions closely related to $E|X_k|^t < \infty$ it is shown that the rate of convergence of $P(|S_N| > \varepsilon)$ to zero is related to $\sum_k |a_{N,k}|^t$. The theorems presented here extend some of the results in the literature to not necessarily independent sequences $\{X_k\}$.


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F. T. Wright. "Rates of Convergence for Weighted Sums of Random Variables." Ann. Math. Statist. 43 (5) 1687 - 1691, October, 1972.


Published: October, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0251.60016
MathSciNet: MR348824
Digital Object Identifier: 10.1214/aoms/1177692403

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 5 • October, 1972
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