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MOMENT ESTIMATION FOR MULTIVARIATE EXTREME VALUE

DISTRIBUTION IN A NESTED LOGISTIC MODEL

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DAOJI SHI^{1} AND SHENGSHENG ZHOU^{2}

^{1} *Department of Mathematics, Tianjin University, Tianjin 300072, China*

^{2} *Department of Mathematics, Anhui Institute of Mechanical and Electrical Engineering,*

Wuhu 241000, China
(Received November 1, 1995; revised February 23, 1998)

**Abstract.**
This paper considers multivariate
extreme value distribution in a nested logistic model. The
dependence structure for this model is discussed. We find a
useful transformation that transformed variables possess the
mixed independence. Thus, the explicit algebraic formulae
for a characteristic function and moments may be given. We
use the method of moments to derive estimators of the
dependence parameters and investigate the properties of these
estimators in large samples via asymptotic theory and in
finite samples via computer simulation. We also compare
moment estimation with a maximum likelihood estimation in
finite sample sizes. The results indicate that moment
estimation is good for all practical purposes.

*Key words and phrases*:
Gumbel distribution,
maximum likelihood estimation, moment estimation,
multivariate extreme value distribution.

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