Publications de l'Institut Mathématique, Nouvelle SérieVol. 86(100), pp. 41–53 (2009)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 86(100), pp. 41–53 (2009) |
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DOMAINS OF ATTRACTION OF THE REAL RANDOM VECTOR $(X,X^2)$ AND APPLICATIONSEdward Omey and Stefan Van GulckDepartment of Mathematics and Statistics, HUB, Brussels, BelgiumAbstract: 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 discussion of the asymptotic behaviour of $SV(n)$ and $t(n)$. Classification (MSC2000): 60E05, 60F05; 62E20, 91B70 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 4 Nov 2009. This page was last modified: 26 Nov 2009.
© 2009 Mathematical Institute of the Serbian Academy of Science and Arts
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