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November, 1982 The Expected Ratio of the Sum of Squares to the Square of the Sum
D. L. McLeish, G. L. O'Brien
Ann. Probab. 10(4): 1019-1028 (November, 1982). DOI: 10.1214/aop/1176993722

Abstract

Let $\{X_i, i = 1,2, \cdots\}$ be a sequence of positive i.i.d. random variables. Define $S_n = \sum^n_{i=1} X_i$ and $T_n = \sum^n_{i=1} X^2_i$. We study the rate, if any, at which $E\lbrack S^{-2}_n T_n\rbrack \rightarrow 0$.

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D. L. McLeish. G. L. O'Brien. "The Expected Ratio of the Sum of Squares to the Square of the Sum." Ann. Probab. 10 (4) 1019 - 1028, November, 1982. https://doi.org/10.1214/aop/1176993722

Information

Published: November, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0545.60034
MathSciNet: MR672301
Digital Object Identifier: 10.1214/aop/1176993722

Subjects:
Primary: 60F99

Keywords: expectation , limit theorems

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 4 • November, 1982
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