Geodesic
Domains of attraction of the real random vector $(X,X^2)$ and applications
Publications de l'Institut Mathématique, _N_S_86 (2009) no. 100, p. 41 .

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Many statistics are based on functions of sample moments.Important examples are the sample variance $s^2(n)$, the sample coefficient of variation $SV(n)$,the sample dispersion $SD(n)$ and the non-central $t$-statistic $t(n)$.The definition of these quantities makes clear that the vector defined by$\big(\sum_{i=1}^n\!X_i^{},\,\sum_{i=1}^n\!X_i^2\big)$plays an important role.In the paper we obtain conditions under which the vector $(X,X^2)$belongs to a bivariate domain of attraction of a stable law.Applying simple transformations then leads to a full discussionof the asymptotic behaviour of $SV(n)$ and $t(n)$.
DOI : 10.2298/PIM0900041O
Classification : 60E05 60F05 62E20 91B70 
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Edward Omey; Stefan Van Gulck. Domains of attraction of the real random vector $(X,X^2)$ and applications. Publications de l'Institut Mathématique, _N_S_86 (2009) no. 100, p. 41 . doi : 10.2298/PIM0900041O. http://geodesic.mathdoc.fr/articles/10.2298/PIM0900041O/

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