The Expected Ratio of the Sum of Squares to the Square of the Sum

McLeish, D. L.; O'Brien, G. L.

Ann. Probab., Tome 10 (1982) no. 4, p. 1019-1028 / Harvested from Project Euclid

Résumé

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

Publié le : 1982-11-14
Classification: Limit theorems, expectation, 60F99

@article{1176993722,
     author = {McLeish, D. L. and O'Brien, G. L.},
     title = {The Expected Ratio of the Sum of Squares to the Square of the Sum},
     journal = {Ann. Probab.},
     volume = {10},
     number = {4},
     year = {1982},
     pages = { 1019-1028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993722}
}

McLeish, D. L.; O'Brien, G. L. The Expected Ratio of the Sum of Squares to the Square of the Sum. Ann. Probab., Tome 10 (1982) no. 4, pp.  1019-1028. http://gdmltest.u-ga.fr/item/1176993722/