Expectation of the Ratio of the Sum of Squares to the Square of the Sum: Exact and Asymptotic Results

By A. Fuchs, A. Joffe, Jozef L. Teugels. 2002

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Interpreting support vector machine models for multivariate group wise analysis in neuroimaging (2015, neutral): “We refer the interested reader to references (McLeish and O’Brien, 1982; Ladoucette, 2007; Fuchs et al., 2002) where the behavior above ratio has been treated with far more rigor.”
Asymptotic behavior of the moments of the ratio of the random sum of squares to the square of the random sum (2007, result): “An asymptotic analysis of Tn is provided by Albrecher and Teugels [1], assuming the distribution function F of X1 to be of Pareto-type with positive index α. In particular, they determine limits in distribution for the properly normalized quantity Tn and derive the limiting behavior of arbitrary mom”
Bibliography on stable distributions, processes and related topics (2004, background): “Gabaix, X. (2009). Power laws in economics and finance.”