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 $E\lbrack S^{-2}_n T_n\rbrack \rightarrow 0$.
Citation
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
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