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 $t(n)$.
@article{10_2298_PIM0900041O,
author = {Edward Omey and Stefan Van Gulck},
title = {Domains of attraction of the real random vector $(X,X^2)$ and applications},
journal = {Publications de l'Institut Math\'ematique},
pages = {41 },
publisher = {mathdoc},
volume = {_N_S_86},
number = {100},
year = {2009},
doi = {10.2298/PIM0900041O},
zbl = {1265.60011},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0900041O/}
}
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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
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