MOMENT ESTIMATION FOR MULTIVARIATE EXTREME VALUE DISTRIBUTION IN A NESTED LOGISTIC MODEL

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

1Department of Mathematics, Tianjin University, Tianjin 300072, China 2Department 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.