Open Access
Translator Disclaimer
August, 1979 Asymptotic Independence in the Multivariate Central Limit Theorem
William N. Hudson, Howard G. Tucker
Ann. Probab. 7(4): 662-671 (August, 1979). DOI: 10.1214/aop/1176994989


Necessary and sufficient conditions are given for asymptotic independence in the multivariate central limit theorem. If $\{X_n\}$ is a sequence of independent, identically distributed random variables whose common distribution is symmetric, and if the distribution of $X^2_1$ is in the domain of attraction of a stable distribution of characteristic exponent $\alpha$, then $\bar{X}$ and $s^2$ are asymptotically independent if and only if $1 \leqslant \alpha \leqslant 2$. If the components of a multivariate infinitely divisible distribution are pairwise independent, then they are independent.


Download Citation

William N. Hudson. Howard G. Tucker. "Asymptotic Independence in the Multivariate Central Limit Theorem." Ann. Probab. 7 (4) 662 - 671, August, 1979.


Published: August, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0411.60028
MathSciNet: MR537213
Digital Object Identifier: 10.1214/aop/1176994989

Primary: 60F05

Keywords: Asymptotic independence , multivariate central limit theorem , stable distributions and their domains of attraction

Rights: Copyright © 1979 Institute of Mathematical Statistics


Vol.7 • No. 4 • August, 1979
Back to Top